linear_algebra.linear_independent | Mathlib porting status

(last sync)

chore(data/finset/lattice): Move lemmas around (#18900)

Move map_finset_sup/map_finset_inf from order.hom.lattice to data.finset.lattice. This breaks a few unqualified downstream uses of submodule.map_bot.

Diff

@@ -365,8 +365,8 @@ by apply @linear_independent_comp_subtype_disjoint _ _ _ id
 
 theorem linear_independent_iff_total_on {s : set M} :
   linear_independent R (λ x, x : s → M) ↔ (finsupp.total_on M M R id s).ker = ⊥ :=
-by rw [finsupp.total_on, linear_map.ker, linear_map.comap_cod_restrict, map_bot, comap_bot,
-  linear_map.ker_comp, linear_independent_subtype_disjoint, disjoint_iff_inf_le,
+by rw [finsupp.total_on, linear_map.ker, linear_map.comap_cod_restrict, submodule.map_bot,
+  comap_bot, linear_map.ker_comp, linear_independent_subtype_disjoint, disjoint_iff_inf_le,
   ← map_comap_subtype, map_le_iff_le_comap, comap_bot, ker_subtype, le_bot_iff]
 
 lemma linear_independent.restrict_of_comp_subtype {s : set ι}
@@ -710,7 +710,7 @@ begin
   { rw [← linear_map.ker_eq_bot, linear_map.ker_cod_restrict],
     apply hv },
   { rw [← linear_map.range_eq_top, linear_map.range_eq_map, linear_map.map_cod_restrict,
-      ← linear_map.range_le_iff_comap, range_subtype, map_top],
+      ← linear_map.range_le_iff_comap, range_subtype, submodule.map_top],
     rw finsupp.range_total,
     exact le_rfl },
   { intro l,

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -141,7 +141,7 @@ theorem linearIndependent_iff' :
 #align linear_independent_iff' linearIndependent_iff'
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (i «expr ∉ » s) -/
 #print linearIndependent_iff'' /-
 theorem linearIndependent_iff'' :
     LinearIndependent R v ↔
@@ -507,7 +507,7 @@ theorem LinearIndependent.mono {t s : Set M} (h : t ⊆ s) :
 #align linear_independent.mono LinearIndependent.mono
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print linearIndependent_of_finite /-
 theorem linearIndependent_of_finite (s : Set M)
     (H : ∀ (t) (_ : t ⊆ s), Set.Finite t → LinearIndependent R (fun x => x : t → M)) :
@@ -1061,7 +1061,7 @@ theorem exists_maximal_independent' (s : ι → M) :
 #align exists_maximal_independent' exists_maximal_independent'
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i «expr ∉ » I) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (i «expr ∉ » I) -/
 #print exists_maximal_independent /-
 theorem exists_maximal_independent (s : ι → M) :
     ∃ I : Set ι,
@@ -1493,7 +1493,7 @@ theorem linearIndependent_fin2 {f : Fin 2 → V} :
 #align linear_independent_fin2 linearIndependent_fin2
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (b «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (b «expr ⊆ » t) -/
 #print exists_linearIndependent_extension /-
 theorem exists_linearIndependent_extension (hs : LinearIndependent K (coe : s → V)) (hst : s ⊆ t) :
     ∃ (b : _) (_ : b ⊆ t), s ⊆ b ∧ t ⊆ span K b ∧ LinearIndependent K (coe : b → V) :=
@@ -1514,7 +1514,7 @@ theorem exists_linearIndependent_extension (hs : LinearIndependent K (coe : s 
 
 variable (K t)
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (b «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (b «expr ⊆ » t) -/
 #print exists_linearIndependent /-
 theorem exists_linearIndependent :
     ∃ (b : _) (_ : b ⊆ t), span K b = span K t ∧ LinearIndependent K (coe : b → V) :=

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -247,9 +247,9 @@ theorem LinearIndependent.map (hv : LinearIndependent R v) {f : M →ₗ[R] M'}
   by
   rw [disjoint_iff_inf_le, ← Set.image_univ, Finsupp.span_image_eq_map_total,
     map_inf_eq_map_inf_comap, map_le_iff_le_comap, comap_bot, Finsupp.supported_univ, top_inf_eq] at
-    hf_inj 
+    hf_inj
   unfold LinearIndependent at hv ⊢
-  rw [hv, le_bot_iff] at hf_inj 
+  rw [hv, le_bot_iff] at hf_inj
   haveI : Inhabited M := ⟨0⟩
   rw [Finsupp.total_comp, @Finsupp.lmapDomain_total _ _ R _ _ _ _ _ _ _ _ _ _ f, LinearMap.ker_comp,
     hf_inj]
@@ -341,12 +341,12 @@ theorem LinearIndependent.fin_cons' {m : ℕ} (x : M) (v : Fin m → M) (hli : L
   by
   rw [Fintype.linearIndependent_iff] at hli ⊢
   rintro g total_eq j
-  simp_rw [Fin.sum_univ_succ, Fin.cons_zero, Fin.cons_succ] at total_eq 
+  simp_rw [Fin.sum_univ_succ, Fin.cons_zero, Fin.cons_succ] at total_eq
   have : g 0 = 0 :=
     by
     refine' x_ortho (g 0) ⟨∑ i : Fin m, g i.succ • v i, _⟩ total_eq
     exact sum_mem fun i _ => smul_mem _ _ (subset_span ⟨i, rfl⟩)
-  rw [this, zero_smul, zero_add] at total_eq 
+  rw [this, zero_smul, zero_add] at total_eq
   exact Fin.cases this (hli _ total_eq) j
 #align linear_independent.fin_cons' LinearIndependent.fin_cons'
 -/
@@ -377,12 +377,12 @@ theorem linearIndependent_finset_map_embedding_subtype (s : Set M)
   let f : t.map (embedding.subtype s) → s := fun x =>
     ⟨x.1, by
       obtain ⟨x, h⟩ := x
-      rw [Finset.mem_map] at h 
+      rw [Finset.mem_map] at h
       obtain ⟨a, ha, rfl⟩ := h
       simp only [Subtype.coe_prop, embedding.coe_subtype]⟩
   convert LinearIndependent.comp li f _
   rintro ⟨x, hx⟩ ⟨y, hy⟩
-  rw [Finset.mem_map] at hx hy 
+  rw [Finset.mem_map] at hx hy
   obtain ⟨a, ha, rfl⟩ := hx
   obtain ⟨b, hb, rfl⟩ := hy
   simp only [imp_self, Subtype.mk_eq_mk]
@@ -591,7 +591,7 @@ theorem LinearIndependent.injective [Nontrivial R] (hv : LinearIndependent R v)
     simp [hij]
   have h_single_eq : Finsupp.single i (1 : R) = Finsupp.single j 1 :=
     by
-    rw [linearIndependent_iff] at hv 
+    rw [linearIndependent_iff] at hv
     simp [eq_add_of_sub_eq' (hv l h_total)]
   simpa [Finsupp.single_eq_single_iff] using h_single_eq
 #align linear_independent.injective LinearIndependent.injective
@@ -693,13 +693,13 @@ theorem LinearIndependent.maximal_iff {ι : Type w} {R : Type u} [Ring R] [Nontr
   fconstructor
   · rintro p κ w i' j rfl
     specialize p (range w) i'.coe_range (range_comp_subset_range _ _)
-    rw [range_comp, ← @image_univ _ _ w] at p 
+    rw [range_comp, ← @image_univ _ _ w] at p
     exact range_iff_surjective.mp (image_injective.mpr i'.injective p)
   · intro p w i' h
     specialize p w (coe : w → M) i' (fun i => ⟨v i, range_subset_iff.mp h i⟩) (by ext; simp)
     have q := congr_arg (fun s => (coe : w → M) '' s) p.range_eq
-    dsimp at q 
-    rw [← image_univ, image_image] at q 
+    dsimp at q
+    rw [← image_univ, image_image] at q
     simpa using q
 #align linear_independent.maximal_iff LinearIndependent.maximal_iff
 -/
@@ -719,7 +719,7 @@ theorem LinearIndependent.eq_of_smul_apply_eq_smul_apply {M : Type _} [AddCommGr
     simp [h]
   have h_single_eq : Finsupp.single i c = Finsupp.single j d :=
     by
-    rw [linearIndependent_iff] at li 
+    rw [linearIndependent_iff] at li
     simp [eq_add_of_sub_eq' (li l h_total)]
   rcases(Finsupp.single_eq_single_iff _ _ _ _).mp h_single_eq with (⟨this, _⟩ | ⟨hc, _⟩)
   · exact this
@@ -738,7 +738,7 @@ theorem LinearIndependent.disjoint_span_image (hv : LinearIndependent R v) {s t
   by
   simp only [disjoint_def, Finsupp.mem_span_image_iff_total]
   rintro _ ⟨l₁, hl₁, rfl⟩ ⟨l₂, hl₂, H⟩
-  rw [hv.injective_total.eq_iff] at H ; subst l₂
+  rw [hv.injective_total.eq_iff] at H; subst l₂
   have : l₁ = 0 := submodule.disjoint_def.mp (Finsupp.disjoint_supported_supported hs) _ hl₁ hl₂
   simp [this]
 #align linear_independent.disjoint_span_image LinearIndependent.disjoint_span_image
@@ -766,9 +766,9 @@ theorem LinearIndependent.total_ne_of_not_mem_support [Nontrivial R] (hv : Linea
   replace h : x ∉ (f.support : Set ι) := h
   have p := hv.not_mem_span_image h
   intro w
-  rw [← w] at p 
-  rw [Finsupp.span_image_eq_map_total] at p 
-  simp only [not_exists, not_and, mem_map] at p 
+  rw [← w] at p
+  rw [Finsupp.span_image_eq_map_total] at p
+  simp only [not_exists, not_and, mem_map] at p
   exact p f (f.mem_supported_support R) rfl
 #align linear_independent.total_ne_of_not_mem_support LinearIndependent.total_ne_of_not_mem_support
 -/
@@ -798,12 +798,12 @@ theorem linearIndependent_sum {v : Sum ι ι' → M} :
     rw [Finset.sum_preimage', Finset.sum_preimage', ← Finset.sum_union, ← Finset.filter_or]
     · simpa only [← mem_union, range_inl_union_range_inr, mem_univ, Finset.filter_True]
     · exact Finset.disjoint_filter.2 fun x _ hx => disjoint_left.1 is_compl_range_inl_range_inr.1 hx
-  · rw [← eq_neg_iff_add_eq_zero] at this 
-    rw [disjoint_def'] at hlr 
+  · rw [← eq_neg_iff_add_eq_zero] at this
+    rw [disjoint_def'] at hlr
     have A := hlr _ (sum_mem fun i hi => _) _ (neg_mem <| sum_mem fun i hi => _) this
     · cases' i with i i
       · exact hl _ _ A i (Finset.mem_preimage.2 hi)
-      · rw [this, neg_eq_zero] at A 
+      · rw [this, neg_eq_zero] at A
         exact hr _ _ A i (Finset.mem_preimage.2 hi)
     · exact smul_mem _ _ (subset_span ⟨Sum.inl i, mem_range_self _, rfl⟩)
     · exact smul_mem _ _ (subset_span ⟨Sum.inr i, mem_range_self _, rfl⟩)
@@ -871,7 +871,7 @@ theorem linearIndependent_iUnion_finite {η : Type _} {ιs : η → Type _} {f :
           disjoint_def.1 (hd x₁ {y₁} (finite_singleton y₁) fun h => h_cases (eq_of_mem_singleton h))
             (f x₁ x₂) (subset_span (mem_range_self _))
         rw [iSup_singleton]
-        simp only at hxy 
+        simp only at hxy
         rw [hxy]
         exact subset_span (mem_range_self y₂)
       exact False.elim ((hindep x₁).NeZero _ h0)
@@ -954,7 +954,7 @@ theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M
     rfl
   have : (LinearIndependent.totalEquiv hv : (ι →₀ R) →ₗ[R] span R (range v)) l = x :=
     by
-    rw [Eq] at this 
+    rw [Eq] at this
     exact Subtype.ext_iff.2 this
   rw [← LinearEquiv.symm_apply_apply hv.total_equiv l]
   rw [← this]
@@ -992,9 +992,9 @@ theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
 theorem linearIndependent_iff_not_smul_mem_span :
     LinearIndependent R v ↔ ∀ (i : ι) (a : R), a • v i ∈ span R (v '' (univ \ {i})) → a = 0 :=
   ⟨fun hv i a ha => by
-    rw [Finsupp.span_image_eq_map_total, mem_map] at ha 
+    rw [Finsupp.span_image_eq_map_total, mem_map] at ha
     rcases ha with ⟨l, hl, e⟩
-    rw [sub_eq_zero.1 (linearIndependent_iff.1 hv (l - Finsupp.single i a) (by simp [e]))] at hl 
+    rw [sub_eq_zero.1 (linearIndependent_iff.1 hv (l - Finsupp.single i a) (by simp [e]))] at hl
     by_contra hn
     exact (not_mem_of_mem_diff (hl <| by simp [hn])) (mem_singleton _), fun H =>
     linearIndependent_iff.2 fun l hl => by
@@ -1020,7 +1020,7 @@ theorem LinearIndependent.independent_span_singleton (hv : LinearIndependent R v
   refine' complete_lattice.independent_def.mp fun i => _
   rw [disjoint_iff_inf_le]
   intro m hm
-  simp only [mem_inf, mem_span_singleton, iSup_subtype', ← span_range_eq_supr] at hm 
+  simp only [mem_inf, mem_span_singleton, iSup_subtype', ← span_range_eq_supr] at hm
   obtain ⟨⟨r, rfl⟩, hm⟩ := hm
   suffices r = 0 by simp [this]
   apply linear_independent_iff_not_smul_mem_span.mp hv i
@@ -1079,7 +1079,7 @@ theorem exists_maximal_independent (s : ι → M) :
   have h := mt hImaximal _
   swap
   · intro h2
-    rw [h2] at hi 
+    rw [h2] at hi
     exact absurd hiJ hi
   obtain ⟨f, supp_f, sum_f, f_ne⟩ := linear_dependent_comp_subtype.mp h
   have hfi : f i ≠ 0 := by
@@ -1093,7 +1093,7 @@ theorem exists_maximal_independent (s : ι → M) :
   use f i, hfi
   have hfi' : i ∈ f.support := finsupp.mem_support_iff.mpr hfi
   rw [← Finset.insert_erase hfi', Finset.sum_insert (Finset.not_mem_erase _ _),
-    add_eq_zero_iff_eq_neg] at sum_f 
+    add_eq_zero_iff_eq_neg] at sum_f
   rw [sum_f]
   refine' neg_mem (sum_mem fun c hc => smul_mem _ _ (subset_span ⟨c, _, rfl⟩))
   exact (memJ.mp (supp_f (Finset.erase_subset _ _ hc))).resolve_left (Finset.ne_of_mem_erase hc)
@@ -1118,8 +1118,8 @@ theorem surjective_of_linearIndependent_of_span [Nontrivial R] (hv : LinearIndep
   have h_total_eq : (Finsupp.total ι M R v) l = (Finsupp.total ι M R v) (Finsupp.single i 1) := by
     rw [h_total_l, Finsupp.total_single, one_smul]
   have l_eq : l = _ := LinearMap.ker_eq_bot.1 hv h_total_eq
-  dsimp only [l] at l_eq 
-  rw [← Finsupp.embDomain_eq_mapDomain] at l_eq 
+  dsimp only [l] at l_eq
+  rw [← Finsupp.embDomain_eq_mapDomain] at l_eq
   rcases Finsupp.single_of_embDomain_single (repr ⟨v i, _⟩) f i (1 : R) zero_ne_one.symm l_eq with
     ⟨i', hi'⟩
   use i'
@@ -1154,7 +1154,7 @@ theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
     (hs : LinearIndependent R (fun x => x : s → M)) (hf_inj : Disjoint (span R s) f.ker) :
     LinearIndependent R (fun x => x : f '' s → M') :=
   by
-  rw [← @Subtype.range_coe _ s] at hf_inj 
+  rw [← @Subtype.range_coe _ s] at hf_inj
   refine' (hs.map hf_inj).to_subtype_range' _
   simp [Set.range_comp f]
 #align linear_independent.image_subtype LinearIndependent.image_subtype
@@ -1261,7 +1261,7 @@ theorem linearIndependent_monoidHom (G : Type _) [Monoid G] (L : Type _) [CommRi
               _ = (∑ i in insert a s, (g i • i : G → L)) 1 :=
                 by
                 rw [Finset.sum_eq_single a]
-                · intro i his hia; rw [Finset.mem_insert] at his 
+                · intro i his hia; rw [Finset.mem_insert] at his
                   rw [h3 i (his.resolve_left hia), zero_smul]
                 · intro haas; exfalso; apply haas; exact Finset.mem_insert_self a s
               _ = 0 := by rw [hg] <;> rfl
@@ -1592,7 +1592,7 @@ theorem exists_of_linearIndependent_of_finite_span {t : Finset V}
       have hb₁s : b₁ ∉ s := fun h =>
         by
         have : b₁ ∈ s ∩ ↑(insert b₁ t) := ⟨h, Finset.mem_insert_self _ _⟩
-        rwa [hst] at this 
+        rwa [hst] at this
       have hb₁s' : b₁ ∉ s' := fun h => hb₁s <| hs' h
       have hst : s ∩ ↑t = ∅ :=
         eq_empty_of_subset_empty <|
@@ -1616,7 +1616,7 @@ theorem exists_of_linearIndependent_of_finite_span {t : Finset V}
           have : s ⊆ (span K (insert b₁ ↑(s' ∪ t)) : Submodule K V) := by
             simpa [insert_eq, -singleton_union, -union_singleton] using hss'
           have hb₁ : b₁ ∈ span K (insert b₂ ↑(s' ∪ t)) := mem_span_insert_exchange (this hb₂s) hb₂t
-          rw [span_insert_eq_span hb₁] at hb₃  <;> simpa using hb₃
+          rw [span_insert_eq_span hb₁] at hb₃ <;> simpa using hb₃
         let ⟨u, hust, hsu, Eq⟩ := ih _ (by simp [insert_subset, hb₂s, hs']) hst this
         ⟨u, Subset.trans hust <| union_subset_union (Subset.refl _) (by simp [subset_insert]), hsu,
           by simp [Eq, hb₂t', hb₁t, hb₁s']⟩

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -1067,7 +1067,36 @@ theorem exists_maximal_independent (s : ι → M) :
     ∃ I : Set ι,
       (LinearIndependent R fun x : I => s x) ∧
         ∀ (i) (_ : i ∉ I), ∃ a : R, a ≠ 0 ∧ a • s i ∈ span R (s '' I) :=
-  by classical
+  by
+  classical
+  rcases exists_maximal_independent' R s with ⟨I, hIlinind, hImaximal⟩
+  use I, hIlinind
+  intro i hi
+  specialize hImaximal (I ∪ {i}) (by simp)
+  set J := I ∪ {i} with hJ
+  have memJ : ∀ {x}, x ∈ J ↔ x = i ∨ x ∈ I := by simp [hJ]
+  have hiJ : i ∈ J := by simp
+  have h := mt hImaximal _
+  swap
+  · intro h2
+    rw [h2] at hi 
+    exact absurd hiJ hi
+  obtain ⟨f, supp_f, sum_f, f_ne⟩ := linear_dependent_comp_subtype.mp h
+  have hfi : f i ≠ 0 := by
+    contrapose hIlinind
+    refine' linear_dependent_comp_subtype.mpr ⟨f, _, sum_f, f_ne⟩
+    simp only [Finsupp.mem_supported, hJ] at supp_f ⊢
+    rintro x hx
+    refine' (memJ.mp (supp_f hx)).resolve_left _
+    rintro rfl
+    exact hIlinind (finsupp.mem_support_iff.mp hx)
+  use f i, hfi
+  have hfi' : i ∈ f.support := finsupp.mem_support_iff.mpr hfi
+  rw [← Finset.insert_erase hfi', Finset.sum_insert (Finset.not_mem_erase _ _),
+    add_eq_zero_iff_eq_neg] at sum_f 
+  rw [sum_f]
+  refine' neg_mem (sum_mem fun c hc => smul_mem _ _ (subset_span ⟨c, _, rfl⟩))
+  exact (memJ.mp (supp_f (Finset.erase_subset _ _ hc))).resolve_left (Finset.ne_of_mem_erase hc)
 #align exists_maximal_independent exists_maximal_independent
 -/

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -1067,36 +1067,7 @@ theorem exists_maximal_independent (s : ι → M) :
     ∃ I : Set ι,
       (LinearIndependent R fun x : I => s x) ∧
         ∀ (i) (_ : i ∉ I), ∃ a : R, a ≠ 0 ∧ a • s i ∈ span R (s '' I) :=
-  by
-  classical
-  rcases exists_maximal_independent' R s with ⟨I, hIlinind, hImaximal⟩
-  use I, hIlinind
-  intro i hi
-  specialize hImaximal (I ∪ {i}) (by simp)
-  set J := I ∪ {i} with hJ
-  have memJ : ∀ {x}, x ∈ J ↔ x = i ∨ x ∈ I := by simp [hJ]
-  have hiJ : i ∈ J := by simp
-  have h := mt hImaximal _
-  swap
-  · intro h2
-    rw [h2] at hi 
-    exact absurd hiJ hi
-  obtain ⟨f, supp_f, sum_f, f_ne⟩ := linear_dependent_comp_subtype.mp h
-  have hfi : f i ≠ 0 := by
-    contrapose hIlinind
-    refine' linear_dependent_comp_subtype.mpr ⟨f, _, sum_f, f_ne⟩
-    simp only [Finsupp.mem_supported, hJ] at supp_f ⊢
-    rintro x hx
-    refine' (memJ.mp (supp_f hx)).resolve_left _
-    rintro rfl
-    exact hIlinind (finsupp.mem_support_iff.mp hx)
-  use f i, hfi
-  have hfi' : i ∈ f.support := finsupp.mem_support_iff.mpr hfi
-  rw [← Finset.insert_erase hfi', Finset.sum_insert (Finset.not_mem_erase _ _),
-    add_eq_zero_iff_eq_neg] at sum_f 
-  rw [sum_f]
-  refine' neg_mem (sum_mem fun c hc => smul_mem _ _ (subset_span ⟨c, _, rfl⟩))
-  exact (memJ.mp (supp_f (Finset.erase_subset _ _ hc))).resolve_left (Finset.ne_of_mem_erase hc)
+  by classical
 #align exists_maximal_independent exists_maximal_independent
 -/

bump to nightly-2024-01-17-06

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

8ba88f37

Diff

@@ -296,7 +296,7 @@ theorem linearIndependent_of_subsingleton [Subsingleton R] : LinearIndependent R
 #print linearIndependent_equiv /-
 theorem linearIndependent_equiv (e : ι ≃ ι') {f : ι' → M} :
     LinearIndependent R (f ∘ e) ↔ LinearIndependent R f :=
-  ⟨fun h => Function.comp.right_id f ▸ e.self_comp_symm ▸ h.comp _ e.symm.Injective, fun h =>
+  ⟨fun h => Function.comp_id f ▸ e.self_comp_symm ▸ h.comp _ e.symm.Injective, fun h =>
     h.comp _ e.Injective⟩
 #align linear_independent_equiv linearIndependent_equiv
 -/

bump to nightly-2023-12-28-06

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

c30f5587

Diff

@@ -1642,7 +1642,7 @@ theorem exists_finite_card_le_of_finite_of_linearIndependent_of_span (ht : t.Fin
   have : s ⊆ (span K ↑ht.toFinset : Submodule K V) := by simp <;> assumption
   let ⟨u, hust, hsu, Eq⟩ := exists_of_linearIndependent_of_finite_span hs this
   have : s.Finite := u.finite_toSet.Subset hsu
-  ⟨this, by rw [← Eq] <;> exact Finset.card_le_of_subset <| finset.coe_subset.mp <| by simp [hsu]⟩
+  ⟨this, by rw [← Eq] <;> exact Finset.card_le_card <| finset.coe_subset.mp <| by simp [hsu]⟩
 #align exists_finite_card_le_of_finite_of_linear_independent_of_span exists_finite_card_le_of_finite_of_linearIndependent_of_span
 -/

bump to nightly-2023-10-27-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/3365b20c2ffa7c35e47e5209b89ba9abdddf3ffe

0456e92d

Diff

@@ -835,7 +835,7 @@ theorem linearIndependent_iUnion_finite_subtype {ι : Type _} {f : ι → Set M}
   by
   rw [Union_eq_Union_finset f]
   apply linearIndependent_iUnion_of_directed
-  · apply directed_of_sup
+  · apply directed_of_isDirected_le
     exact fun t₁ t₂ ht => Union_mono fun i => Union_subset_Union_const fun h => ht h
   intro t
   induction' t using Finset.induction_on with i s his ih

bump to nightly-2023-10-21-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

a2dc86f8

Diff

@@ -163,7 +163,7 @@ theorem not_linearIndependent_iff :
       ∃ s : Finset ι, ∃ g : ι → R, ∑ i in s, g i • v i = 0 ∧ ∃ i ∈ s, g i ≠ 0 :=
   by
   rw [linearIndependent_iff']
-  simp only [exists_prop, not_forall]
+  simp only [exists_prop, Classical.not_forall]
 #align not_linear_independent_iff not_linearIndependent_iff
 -/

bump to nightly-2023-10-04-06

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

7bd6a14d

Diff

@@ -123,7 +123,7 @@ theorem linearIndependent_iff' :
     ⟨fun hf s g hg i his =>
       have h :=
         hf (∑ i in s, Finsupp.single i (g i)) <| by
-          simpa only [LinearMap.map_sum, Finsupp.total_single] using hg
+          simpa only [map_sum, Finsupp.total_single] using hg
       calc
         g i = (Finsupp.lapply i : (ι →₀ R) →ₗ[R] R) (Finsupp.single i (g i)) := by
           rw [Finsupp.lapply_apply, Finsupp.single_eq_same]

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp, Anne Baanen
 -/
-import Mathbin.Algebra.BigOperators.Fin
-import Mathbin.LinearAlgebra.Finsupp
-import Mathbin.LinearAlgebra.Prod
-import Mathbin.SetTheory.Cardinal.Basic
+import Algebra.BigOperators.Fin
+import LinearAlgebra.Finsupp
+import LinearAlgebra.Prod
+import SetTheory.Cardinal.Basic
 
 #align_import linear_algebra.linear_independent from "leanprover-community/mathlib"@"9d684a893c52e1d6692a504a118bfccbae04feeb"
 
@@ -141,7 +141,7 @@ theorem linearIndependent_iff' :
 #align linear_independent_iff' linearIndependent_iff'
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i «expr ∉ » s) -/
 #print linearIndependent_iff'' /-
 theorem linearIndependent_iff'' :
     LinearIndependent R v ↔
@@ -507,7 +507,7 @@ theorem LinearIndependent.mono {t s : Set M} (h : t ⊆ s) :
 #align linear_independent.mono LinearIndependent.mono
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print linearIndependent_of_finite /-
 theorem linearIndependent_of_finite (s : Set M)
     (H : ∀ (t) (_ : t ⊆ s), Set.Finite t → LinearIndependent R (fun x => x : t → M)) :
@@ -1061,7 +1061,7 @@ theorem exists_maximal_independent' (s : ι → M) :
 #align exists_maximal_independent' exists_maximal_independent'
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » I) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i «expr ∉ » I) -/
 #print exists_maximal_independent /-
 theorem exists_maximal_independent (s : ι → M) :
     ∃ I : Set ι,
@@ -1493,7 +1493,7 @@ theorem linearIndependent_fin2 {f : Fin 2 → V} :
 #align linear_independent_fin2 linearIndependent_fin2
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (b «expr ⊆ » t) -/
 #print exists_linearIndependent_extension /-
 theorem exists_linearIndependent_extension (hs : LinearIndependent K (coe : s → V)) (hst : s ⊆ t) :
     ∃ (b : _) (_ : b ⊆ t), s ⊆ b ∧ t ⊆ span K b ∧ LinearIndependent K (coe : b → V) :=
@@ -1514,7 +1514,7 @@ theorem exists_linearIndependent_extension (hs : LinearIndependent K (coe : s 
 
 variable (K t)
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (b «expr ⊆ » t) -/
 #print exists_linearIndependent /-
 theorem exists_linearIndependent :
     ∃ (b : _) (_ : b ⊆ t), span K b = span K t ∧ LinearIndependent K (coe : b → V) :=

bump to nightly-2023-08-23-23

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

f612b9e0

Diff

@@ -315,7 +315,7 @@ theorem linearIndependent_subtype_range {ι} {f : ι → M} (hf : Injective f) :
 #align linear_independent_subtype_range linearIndependent_subtype_range
 -/
 
-alias linearIndependent_subtype_range ↔ LinearIndependent.of_subtype_range _
+alias ⟨LinearIndependent.of_subtype_range, _⟩ := linearIndependent_subtype_range
 #align linear_independent.of_subtype_range LinearIndependent.of_subtype_range
 
 #print linearIndependent_image /-
@@ -577,7 +577,7 @@ theorem linearIndependent_iff_injective_total :
 #align linear_independent_iff_injective_total linearIndependent_iff_injective_total
 -/
 
-alias linearIndependent_iff_injective_total ↔ LinearIndependent.injective_total _
+alias ⟨LinearIndependent.injective_total, _⟩ := linearIndependent_iff_injective_total
 #align linear_independent.injective_total LinearIndependent.injective_total
 
 #print LinearIndependent.injective /-
@@ -1312,7 +1312,7 @@ theorem linearIndependent_unique_iff (v : ι → M) [Unique ι] :
 #align linear_independent_unique_iff linearIndependent_unique_iff
 -/
 
-alias linearIndependent_unique_iff ↔ _ linearIndependent_unique
+alias ⟨_, linearIndependent_unique⟩ := linearIndependent_unique_iff
 #align linear_independent_unique linearIndependent_unique
 
 #print linearIndependent_singleton /-

bump to nightly-2023-08-02-01

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

7aca3f15

Diff

@@ -1489,7 +1489,7 @@ theorem linearIndependent_fin_succ' {n} {v : Fin (n + 1) → V} :
 theorem linearIndependent_fin2 {f : Fin 2 → V} :
     LinearIndependent K f ↔ f 1 ≠ 0 ∧ ∀ a : K, a • f 1 ≠ f 0 := by
   rw [linearIndependent_fin_succ, linearIndependent_unique_iff, range_unique, mem_span_singleton,
-    not_exists, show Fin.tail f default = f 1 by rw [← Fin.succ_zero_eq_one] <;> rfl]
+    not_exists, show Fin.tail f default = f 1 by rw [← Fin.succ_zero_eq_one'] <;> rfl]
 #align linear_independent_fin2 linearIndependent_fin2
 -/

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp, Anne Baanen
-
-! This file was ported from Lean 3 source module linear_algebra.linear_independent
-! leanprover-community/mathlib commit 9d684a893c52e1d6692a504a118bfccbae04feeb
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.BigOperators.Fin
 import Mathbin.LinearAlgebra.Finsupp
 import Mathbin.LinearAlgebra.Prod
 import Mathbin.SetTheory.Cardinal.Basic
 
+#align_import linear_algebra.linear_independent from "leanprover-community/mathlib"@"9d684a893c52e1d6692a504a118bfccbae04feeb"
+
 /-!
 
 # Linear independence
@@ -144,7 +141,7 @@ theorem linearIndependent_iff' :
 #align linear_independent_iff' linearIndependent_iff'
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
 #print linearIndependent_iff'' /-
 theorem linearIndependent_iff'' :
     LinearIndependent R v ↔
@@ -510,7 +507,7 @@ theorem LinearIndependent.mono {t s : Set M} (h : t ⊆ s) :
 #align linear_independent.mono LinearIndependent.mono
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print linearIndependent_of_finite /-
 theorem linearIndependent_of_finite (s : Set M)
     (H : ∀ (t) (_ : t ⊆ s), Set.Finite t → LinearIndependent R (fun x => x : t → M)) :
@@ -1064,7 +1061,7 @@ theorem exists_maximal_independent' (s : ι → M) :
 #align exists_maximal_independent' exists_maximal_independent'
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i «expr ∉ » I) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » I) -/
 #print exists_maximal_independent /-
 theorem exists_maximal_independent (s : ι → M) :
     ∃ I : Set ι,
@@ -1496,7 +1493,7 @@ theorem linearIndependent_fin2 {f : Fin 2 → V} :
 #align linear_independent_fin2 linearIndependent_fin2
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (b «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ⊆ » t) -/
 #print exists_linearIndependent_extension /-
 theorem exists_linearIndependent_extension (hs : LinearIndependent K (coe : s → V)) (hst : s ⊆ t) :
     ∃ (b : _) (_ : b ⊆ t), s ⊆ b ∧ t ⊆ span K b ∧ LinearIndependent K (coe : b → V) :=
@@ -1517,7 +1514,7 @@ theorem exists_linearIndependent_extension (hs : LinearIndependent K (coe : s 
 
 variable (K t)
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (b «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ⊆ » t) -/
 #print exists_linearIndependent /-
 theorem exists_linearIndependent :
     ∃ (b : _) (_ : b ⊆ t), span K b = span K t ∧ LinearIndependent K (coe : b → V) :=

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -112,10 +112,13 @@ def LinearIndependent : Prop :=
 
 variable {R} {v}
 
+#print linearIndependent_iff /-
 theorem linearIndependent_iff : LinearIndependent R v ↔ ∀ l, Finsupp.total ι M R v l = 0 → l = 0 :=
   by simp [LinearIndependent, LinearMap.ker_eq_bot']
 #align linear_independent_iff linearIndependent_iff
+-/
 
+#print linearIndependent_iff' /-
 theorem linearIndependent_iff' :
     LinearIndependent R v ↔
       ∀ s : Finset ι, ∀ g : ι → R, ∑ i in s, g i • v i = 0 → ∀ i ∈ s, g i = 0 :=
@@ -139,8 +142,10 @@ theorem linearIndependent_iff' :
       Finsupp.ext fun i =>
         by_contradiction fun hni => hni <| hf _ _ hl _ <| Finsupp.mem_support_iff.2 hni⟩
 #align linear_independent_iff' linearIndependent_iff'
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i «expr ∉ » s) -/
+#print linearIndependent_iff'' /-
 theorem linearIndependent_iff'' :
     LinearIndependent R v ↔
       ∀ (s : Finset ι) (g : ι → R) (hg : ∀ (i) (_ : i ∉ s), g i = 0),
@@ -153,7 +158,9 @@ theorem linearIndependent_iff'' :
           (by simp_rw [ite_smul, zero_smul, Finset.sum_extend_by_zero, hg]) i
       exact (if_pos hi).symm⟩
 #align linear_independent_iff'' linearIndependent_iff''
+-/
 
+#print not_linearIndependent_iff /-
 theorem not_linearIndependent_iff :
     ¬LinearIndependent R v ↔
       ∃ s : Finset ι, ∃ g : ι → R, ∑ i in s, g i • v i = 0 ∧ ∃ i ∈ s, g i ≠ 0 :=
@@ -161,7 +168,9 @@ theorem not_linearIndependent_iff :
   rw [linearIndependent_iff']
   simp only [exists_prop, not_forall]
 #align not_linear_independent_iff not_linearIndependent_iff
+-/
 
+#print Fintype.linearIndependent_iff /-
 theorem Fintype.linearIndependent_iff [Fintype ι] :
     LinearIndependent R v ↔ ∀ g : ι → R, ∑ i, g i • v i = 0 → ∀ i, g i = 0 :=
   by
@@ -172,7 +181,9 @@ theorem Fintype.linearIndependent_iff [Fintype ι] :
   refine' (Finset.sum_subset (Finset.subset_univ _) fun i _ hi => _).symm
   rw [hg i hi, zero_smul]
 #align fintype.linear_independent_iff Fintype.linearIndependent_iff
+-/
 
+#print Fintype.linearIndependent_iff' /-
 /-- A finite family of vectors `v i` is linear independent iff the linear map that sends
 `c : ι → R` to `∑ i, c i • v i` has the trivial kernel. -/
 theorem Fintype.linearIndependent_iff' [Fintype ι] :
@@ -180,16 +191,22 @@ theorem Fintype.linearIndependent_iff' [Fintype ι] :
       (LinearMap.lsum R (fun i : ι => R) ℕ fun i => LinearMap.id.smul_right (v i)).ker = ⊥ :=
   by simp [Fintype.linearIndependent_iff, LinearMap.ker_eq_bot', funext_iff] <;> skip
 #align fintype.linear_independent_iff' Fintype.linearIndependent_iff'
+-/
 
+#print Fintype.not_linearIndependent_iff /-
 theorem Fintype.not_linearIndependent_iff [Fintype ι] :
     ¬LinearIndependent R v ↔ ∃ g : ι → R, ∑ i, g i • v i = 0 ∧ ∃ i, g i ≠ 0 := by
   simpa using not_iff_not.2 Fintype.linearIndependent_iff
 #align fintype.not_linear_independent_iff Fintype.not_linearIndependent_iff
+-/
 
+#print linearIndependent_empty_type /-
 theorem linearIndependent_empty_type [IsEmpty ι] : LinearIndependent R v :=
   linearIndependent_iff.mpr fun v hv => Subsingleton.elim v 0
 #align linear_independent_empty_type linearIndependent_empty_type
+-/
 
+#print LinearIndependent.ne_zero /-
 theorem LinearIndependent.ne_zero [Nontrivial R] (i : ι) (hv : LinearIndependent R v) : v i ≠ 0 :=
   fun h =>
   zero_ne_one' R <|
@@ -200,7 +217,9 @@ theorem LinearIndependent.ne_zero [Nontrivial R] (i : ι) (hv : LinearIndependen
         · simp
         · simp [h])
 #align linear_independent.ne_zero LinearIndependent.ne_zero
+-/
 
+#print LinearIndependent.comp /-
 /-- A subfamily of a linearly independent family (i.e., a composition with an injective map) is a
 linearly independent family. -/
 theorem LinearIndependent.comp (h : LinearIndependent R v) (f : ι' → ι) (hf : Injective f) :
@@ -214,11 +233,15 @@ theorem LinearIndependent.comp (h : LinearIndependent R v) (f : ι' → ι) (hf
   convert h_map_domain x
   rw [Finsupp.mapDomain_apply hf]
 #align linear_independent.comp LinearIndependent.comp
+-/
 
+#print LinearIndependent.coe_range /-
 theorem LinearIndependent.coe_range (i : LinearIndependent R v) :
     LinearIndependent R (coe : range v → M) := by simpa using i.comp _ (range_splitting_injective v)
 #align linear_independent.coe_range LinearIndependent.coe_range
+-/
 
+#print LinearIndependent.map /-
 /-- If `v` is a linearly independent family of vectors and the kernel of a linear map `f` is
 disjoint with the submodule spanned by the vectors of `v`, then `f ∘ v` is a linearly independent
 family of vectors. See also `linear_independent.map'` for a special case assuming `ker f = ⊥`. -/
@@ -235,14 +258,18 @@ theorem LinearIndependent.map (hv : LinearIndependent R v) {f : M →ₗ[R] M'}
     hf_inj]
   exact fun _ => rfl
 #align linear_independent.map LinearIndependent.map
+-/
 
+#print LinearIndependent.map' /-
 /-- An injective linear map sends linearly independent families of vectors to linearly independent
 families of vectors. See also `linear_independent.map` for a more general statement. -/
 theorem LinearIndependent.map' (hv : LinearIndependent R v) (f : M →ₗ[R] M') (hf_inj : f.ker = ⊥) :
     LinearIndependent R (f ∘ v) :=
   hv.map <| by simp [hf_inj]
 #align linear_independent.map' LinearIndependent.map'
+-/
 
+#print LinearIndependent.of_comp /-
 /-- If the image of a family of vectors under a linear map is linearly independent, then so is
 the original family. -/
 theorem LinearIndependent.of_comp (f : M →ₗ[R] M') (hfv : LinearIndependent R (f ∘ v)) :
@@ -251,29 +278,38 @@ theorem LinearIndependent.of_comp (f : M →ₗ[R] M') (hfv : LinearIndependent
     have : ∑ i : ι in s, g i • f (v i) = 0 := by simp_rw [← f.map_smul, ← f.map_sum, hg, f.map_zero]
     linearIndependent_iff'.1 hfv s g this i his
 #align linear_independent.of_comp LinearIndependent.of_comp
+-/
 
+#print LinearMap.linearIndependent_iff /-
 /-- If `f` is an injective linear map, then the family `f ∘ v` is linearly independent
 if and only if the family `v` is linearly independent. -/
 protected theorem LinearMap.linearIndependent_iff (f : M →ₗ[R] M') (hf_inj : f.ker = ⊥) :
     LinearIndependent R (f ∘ v) ↔ LinearIndependent R v :=
   ⟨fun h => h.of_comp f, fun h => h.map <| by simp only [hf_inj, disjoint_bot_right]⟩
 #align linear_map.linear_independent_iff LinearMap.linearIndependent_iff
+-/
 
+#print linearIndependent_of_subsingleton /-
 @[nontriviality]
 theorem linearIndependent_of_subsingleton [Subsingleton R] : LinearIndependent R v :=
   linearIndependent_iff.2 fun l hl => Subsingleton.elim _ _
 #align linear_independent_of_subsingleton linearIndependent_of_subsingleton
+-/
 
+#print linearIndependent_equiv /-
 theorem linearIndependent_equiv (e : ι ≃ ι') {f : ι' → M} :
     LinearIndependent R (f ∘ e) ↔ LinearIndependent R f :=
   ⟨fun h => Function.comp.right_id f ▸ e.self_comp_symm ▸ h.comp _ e.symm.Injective, fun h =>
     h.comp _ e.Injective⟩
 #align linear_independent_equiv linearIndependent_equiv
+-/
 
+#print linearIndependent_equiv' /-
 theorem linearIndependent_equiv' (e : ι ≃ ι') {f : ι' → M} {g : ι → M} (h : f ∘ e = g) :
     LinearIndependent R g ↔ LinearIndependent R f :=
   h ▸ linearIndependent_equiv e
 #align linear_independent_equiv' linearIndependent_equiv'
+-/
 
 #print linearIndependent_subtype_range /-
 theorem linearIndependent_subtype_range {ι} {f : ι → M} (hf : Injective f) :
@@ -292,12 +328,15 @@ theorem linearIndependent_image {ι} {s : Set ι} {f : ι → M} (hf : Set.InjOn
 #align linear_independent_image linearIndependent_image
 -/
 
+#print linearIndependent_span /-
 theorem linearIndependent_span (hs : LinearIndependent R v) :
     @LinearIndependent ι R (span R (range v)) (fun i : ι => ⟨v i, subset_span (mem_range_self i)⟩) _
       _ _ :=
   LinearIndependent.of_comp (span R (range v)).Subtype hs
 #align linear_independent_span linearIndependent_span
+-/
 
+#print LinearIndependent.fin_cons' /-
 /-- See `linear_independent.fin_cons` for a family of elements in a vector space. -/
 theorem LinearIndependent.fin_cons' {m : ℕ} (x : M) (v : Fin m → M) (hli : LinearIndependent R v)
     (x_ortho : ∀ (c : R) (y : Submodule.span R (Set.range v)), c • x + y = (0 : M) → c = 0) :
@@ -313,7 +352,9 @@ theorem LinearIndependent.fin_cons' {m : ℕ} (x : M) (v : Fin m → M) (hli : L
   rw [this, zero_smul, zero_add] at total_eq 
   exact Fin.cases this (hli _ total_eq) j
 #align linear_independent.fin_cons' LinearIndependent.fin_cons'
+-/
 
+#print LinearIndependent.restrict_scalars /-
 /-- A set of linearly independent vectors in a module `M` over a semiring `K` is also linearly
 independent over a subring `R` of `K`.
 The implementation uses minimal assumptions about the relationship between `R`, `K` and `M`.
@@ -328,6 +369,7 @@ theorem LinearIndependent.restrict_scalars [Semiring K] [SMulWithZero R K] [Modu
   simp_rw [smul_assoc, one_smul]
   exact hg
 #align linear_independent.restrict_scalars LinearIndependent.restrict_scalars
+-/
 
 #print linearIndependent_finset_map_embedding_subtype /-
 /-- Every finite subset of a linearly independent set is linearly independent. -/
@@ -350,6 +392,7 @@ theorem linearIndependent_finset_map_embedding_subtype (s : Set M)
 #align linear_independent_finset_map_embedding_subtype linearIndependent_finset_map_embedding_subtype
 -/
 
+#print linearIndependent_bounded_of_finset_linearIndependent_bounded /-
 /-- If every finite set of linearly independent vectors has cardinality at most `n`,
 then the same is true for arbitrary sets of linearly independent vectors.
 -/
@@ -364,12 +407,14 @@ theorem linearIndependent_bounded_of_finset_linearIndependent_bounded {n : ℕ}
   apply H
   apply linearIndependent_finset_map_embedding_subtype _ li
 #align linear_independent_bounded_of_finset_linear_independent_bounded linearIndependent_bounded_of_finset_linearIndependent_bounded
+-/
 
 section Subtype
 
 /-! The following lemmas use the subtype defined by a set in `M` as the index set `ι`. -/
 
 
+#print linearIndependent_comp_subtype /-
 theorem linearIndependent_comp_subtype {s : Set ι} :
     LinearIndependent R (v ∘ coe : s → M) ↔
       ∀ l ∈ Finsupp.supported R R s, (Finsupp.total ι M R v) l = 0 → l = 0 :=
@@ -387,49 +432,64 @@ theorem linearIndependent_comp_subtype {s : Set ι} :
     · rwa [Finsupp.embDomain_eq_mapDomain, Finsupp.sum_mapDomain_index]
       exacts [fun _ => zero_smul _ _, fun _ _ _ => add_smul _ _ _]
 #align linear_independent_comp_subtype linearIndependent_comp_subtype
+-/
 
+#print linearDependent_comp_subtype' /-
 theorem linearDependent_comp_subtype' {s : Set ι} :
     ¬LinearIndependent R (v ∘ coe : s → M) ↔
       ∃ f : ι →₀ R, f ∈ Finsupp.supported R R s ∧ Finsupp.total ι M R v f = 0 ∧ f ≠ 0 :=
   by simp [linearIndependent_comp_subtype]
 #align linear_dependent_comp_subtype' linearDependent_comp_subtype'
+-/
 
+#print linearDependent_comp_subtype /-
 /-- A version of `linear_dependent_comp_subtype'` with `finsupp.total` unfolded. -/
 theorem linearDependent_comp_subtype {s : Set ι} :
     ¬LinearIndependent R (v ∘ coe : s → M) ↔
       ∃ f : ι →₀ R, f ∈ Finsupp.supported R R s ∧ ∑ i in f.support, f i • v i = 0 ∧ f ≠ 0 :=
   linearDependent_comp_subtype'
 #align linear_dependent_comp_subtype linearDependent_comp_subtype
+-/
 
+#print linearIndependent_subtype /-
 theorem linearIndependent_subtype {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
       ∀ l ∈ Finsupp.supported R R s, (Finsupp.total M M R id) l = 0 → l = 0 :=
   by apply @linearIndependent_comp_subtype _ _ _ id
 #align linear_independent_subtype linearIndependent_subtype
+-/
 
+#print linearIndependent_comp_subtype_disjoint /-
 theorem linearIndependent_comp_subtype_disjoint {s : Set ι} :
     LinearIndependent R (v ∘ coe : s → M) ↔
       Disjoint (Finsupp.supported R R s) (Finsupp.total ι M R v).ker :=
   by rw [linearIndependent_comp_subtype, LinearMap.disjoint_ker]
 #align linear_independent_comp_subtype_disjoint linearIndependent_comp_subtype_disjoint
+-/
 
+#print linearIndependent_subtype_disjoint /-
 theorem linearIndependent_subtype_disjoint {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
       Disjoint (Finsupp.supported R R s) (Finsupp.total M M R id).ker :=
   by apply @linearIndependent_comp_subtype_disjoint _ _ _ id
 #align linear_independent_subtype_disjoint linearIndependent_subtype_disjoint
+-/
 
+#print linearIndependent_iff_totalOn /-
 theorem linearIndependent_iff_totalOn {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔ (Finsupp.totalOn M M R id s).ker = ⊥ := by
   rw [Finsupp.totalOn, LinearMap.ker, LinearMap.comap_codRestrict, Submodule.map_bot, comap_bot,
     LinearMap.ker_comp, linearIndependent_subtype_disjoint, disjoint_iff_inf_le, ←
     map_comap_subtype, map_le_iff_le_comap, comap_bot, ker_subtype, le_bot_iff]
 #align linear_independent_iff_total_on linearIndependent_iff_totalOn
+-/
 
+#print LinearIndependent.restrict_of_comp_subtype /-
 theorem LinearIndependent.restrict_of_comp_subtype {s : Set ι}
     (hs : LinearIndependent R (v ∘ coe : s → M)) : LinearIndependent R (s.restrict v) :=
   hs
 #align linear_independent.restrict_of_comp_subtype LinearIndependent.restrict_of_comp_subtype
+-/
 
 variable (R M)
 
@@ -512,15 +572,18 @@ variable [Module R M] [Module R M'] [Module R M'']
 
 variable {a b : R} {x y : M}
 
+#print linearIndependent_iff_injective_total /-
 theorem linearIndependent_iff_injective_total :
     LinearIndependent R v ↔ Function.Injective (Finsupp.total ι M R v) :=
   linearIndependent_iff.trans
     (injective_iff_map_eq_zero (Finsupp.total ι M R v).toAddMonoidHom).symm
 #align linear_independent_iff_injective_total linearIndependent_iff_injective_total
+-/
 
 alias linearIndependent_iff_injective_total ↔ LinearIndependent.injective_total _
 #align linear_independent.injective_total LinearIndependent.injective_total
 
+#print LinearIndependent.injective /-
 theorem LinearIndependent.injective [Nontrivial R] (hv : LinearIndependent R v) : Injective v :=
   by
   intro i j hij
@@ -535,19 +598,25 @@ theorem LinearIndependent.injective [Nontrivial R] (hv : LinearIndependent R v)
     simp [eq_add_of_sub_eq' (hv l h_total)]
   simpa [Finsupp.single_eq_single_iff] using h_single_eq
 #align linear_independent.injective LinearIndependent.injective
+-/
 
+#print LinearIndependent.to_subtype_range /-
 theorem LinearIndependent.to_subtype_range {ι} {f : ι → M} (hf : LinearIndependent R f) :
     LinearIndependent R (coe : range f → M) :=
   by
   nontriviality R
   exact (linearIndependent_subtype_range hf.injective).2 hf
 #align linear_independent.to_subtype_range LinearIndependent.to_subtype_range
+-/
 
+#print LinearIndependent.to_subtype_range' /-
 theorem LinearIndependent.to_subtype_range' {ι} {f : ι → M} (hf : LinearIndependent R f) {t}
     (ht : range f = t) : LinearIndependent R (coe : t → M) :=
   ht ▸ hf.to_subtype_range
 #align linear_independent.to_subtype_range' LinearIndependent.to_subtype_range'
+-/
 
+#print LinearIndependent.image_of_comp /-
 theorem LinearIndependent.image_of_comp {ι ι'} (s : Set ι) (f : ι → ι') (g : ι' → M)
     (hs : LinearIndependent R fun x : s => g (f x)) : LinearIndependent R fun x : f '' s => g x :=
   by
@@ -555,12 +624,16 @@ theorem LinearIndependent.image_of_comp {ι ι'} (s : Set ι) (f : ι → ι') (
   have : inj_on f s := inj_on_iff_injective.2 hs.injective.of_comp
   exact (linearIndependent_equiv' (Equiv.Set.imageOfInjOn f s this) rfl).1 hs
 #align linear_independent.image_of_comp LinearIndependent.image_of_comp
+-/
 
+#print LinearIndependent.image /-
 theorem LinearIndependent.image {ι} {s : Set ι} {f : ι → M}
     (hs : LinearIndependent R fun x : s => f x) : LinearIndependent R fun x : f '' s => (x : M) :=
   by convert LinearIndependent.image_of_comp s f id hs
 #align linear_independent.image LinearIndependent.image
+-/
 
+#print LinearIndependent.group_smul /-
 theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulAction G R]
     [DistribMulAction G M] [IsScalarTower G R M] [SMulCommClass G R M] {v : ι → M}
     (hv : LinearIndependent R v) (w : ι → G) : LinearIndependent R (w • v) :=
@@ -574,7 +647,9 @@ theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulActi
   · rw [← hsum, Finset.sum_congr rfl _]
     intros; erw [Pi.smul_apply, smul_assoc, smul_comm]
 #align linear_independent.group_smul LinearIndependent.group_smul
+-/
 
+#print LinearIndependent.units_smul /-
 -- This lemma cannot be proved with `linear_independent.group_smul` since the action of
 -- `Rˣ` on `R` is not commutative.
 theorem LinearIndependent.units_smul {v : ι → M} (hv : LinearIndependent R v) (w : ι → Rˣ) :
@@ -591,6 +666,7 @@ theorem LinearIndependent.units_smul {v : ι → M} (hv : LinearIndependent R v)
     erw [Pi.smul_apply, smul_assoc]
     rfl
 #align linear_independent.units_smul LinearIndependent.units_smul
+-/
 
 section Maximal
 
@@ -633,6 +709,7 @@ theorem LinearIndependent.maximal_iff {ι : Type w} {R : Type u} [Ring R] [Nontr
 
 end Maximal
 
+#print LinearIndependent.eq_of_smul_apply_eq_smul_apply /-
 /-- Linear independent families are injective, even if you multiply either side. -/
 theorem LinearIndependent.eq_of_smul_apply_eq_smul_apply {M : Type _} [AddCommGroup M] [Module R M]
     {v : ι → M} (li : LinearIndependent R v) (c d : R) (i j : ι) (hc : c ≠ 0)
@@ -651,12 +728,14 @@ theorem LinearIndependent.eq_of_smul_apply_eq_smul_apply {M : Type _} [AddCommGr
   · exact this
   · contradiction
 #align linear_independent.eq_of_smul_apply_eq_smul_apply LinearIndependent.eq_of_smul_apply_eq_smul_apply
+-/
 
 section Subtype
 
 /-! The following lemmas use the subtype defined by a set in `M` as the index set `ι`. -/
 
 
+#print LinearIndependent.disjoint_span_image /-
 theorem LinearIndependent.disjoint_span_image (hv : LinearIndependent R v) {s t : Set ι}
     (hs : Disjoint s t) : Disjoint (Submodule.span R <| v '' s) (Submodule.span R <| v '' t) :=
   by
@@ -666,7 +745,9 @@ theorem LinearIndependent.disjoint_span_image (hv : LinearIndependent R v) {s t
   have : l₁ = 0 := submodule.disjoint_def.mp (Finsupp.disjoint_supported_supported hs) _ hl₁ hl₂
   simp [this]
 #align linear_independent.disjoint_span_image LinearIndependent.disjoint_span_image
+-/
 
+#print LinearIndependent.not_mem_span_image /-
 theorem LinearIndependent.not_mem_span_image [Nontrivial R] (hv : LinearIndependent R v) {s : Set ι}
     {x : ι} (h : x ∉ s) : v x ∉ Submodule.span R (v '' s) :=
   by
@@ -679,7 +760,9 @@ theorem LinearIndependent.not_mem_span_image [Nontrivial R] (hv : LinearIndepend
   refine' disjoint_def.1 (hv.disjoint_span_image _) (v x) h' w
   simpa using h
 #align linear_independent.not_mem_span_image LinearIndependent.not_mem_span_image
+-/
 
+#print LinearIndependent.total_ne_of_not_mem_support /-
 theorem LinearIndependent.total_ne_of_not_mem_support [Nontrivial R] (hv : LinearIndependent R v)
     {x : ι} (f : ι →₀ R) (h : x ∉ f.support) : Finsupp.total ι M R v f ≠ v x :=
   by
@@ -691,7 +774,9 @@ theorem LinearIndependent.total_ne_of_not_mem_support [Nontrivial R] (hv : Linea
   simp only [not_exists, not_and, mem_map] at p 
   exact p f (f.mem_supported_support R) rfl
 #align linear_independent.total_ne_of_not_mem_support LinearIndependent.total_ne_of_not_mem_support
+-/
 
+#print linearIndependent_sum /-
 theorem linearIndependent_sum {v : Sum ι ι' → M} :
     LinearIndependent R v ↔
       LinearIndependent R (v ∘ Sum.inl) ∧
@@ -726,20 +811,26 @@ theorem linearIndependent_sum {v : Sum ι ι' → M} :
     · exact smul_mem _ _ (subset_span ⟨Sum.inl i, mem_range_self _, rfl⟩)
     · exact smul_mem _ _ (subset_span ⟨Sum.inr i, mem_range_self _, rfl⟩)
 #align linear_independent_sum linearIndependent_sum
+-/
 
+#print LinearIndependent.sum_type /-
 theorem LinearIndependent.sum_type {v' : ι' → M} (hv : LinearIndependent R v)
     (hv' : LinearIndependent R v')
     (h : Disjoint (Submodule.span R (range v)) (Submodule.span R (range v'))) :
     LinearIndependent R (Sum.elim v v') :=
   linearIndependent_sum.2 ⟨hv, hv', h⟩
 #align linear_independent.sum_type LinearIndependent.sum_type
+-/
 
+#print LinearIndependent.union /-
 theorem LinearIndependent.union {s t : Set M} (hs : LinearIndependent R (fun x => x : s → M))
     (ht : LinearIndependent R (fun x => x : t → M)) (hst : Disjoint (span R s) (span R t)) :
     LinearIndependent R (fun x => x : s ∪ t → M) :=
   (hs.sum_type ht <| by simpa).to_subtype_range' <| by simp
 #align linear_independent.union LinearIndependent.union
+-/
 
+#print linearIndependent_iUnion_finite_subtype /-
 theorem linearIndependent_iUnion_finite_subtype {ι : Type _} {f : ι → Set M}
     (hl : ∀ i, LinearIndependent R (fun x => x : f i → M))
     (hd : ∀ i, ∀ t : Set ι, t.Finite → i ∉ t → Disjoint (span R (f i)) (⨆ i ∈ t, span R (f i))) :
@@ -758,7 +849,9 @@ theorem linearIndependent_iUnion_finite_subtype {ι : Type _} {f : ι → Set M}
     rw [span_Union₂]
     exact hd i s s.finite_to_set his
 #align linear_independent_Union_finite_subtype linearIndependent_iUnion_finite_subtype
+-/
 
+#print linearIndependent_iUnion_finite /-
 theorem linearIndependent_iUnion_finite {η : Type _} {ιs : η → Type _} {f : ∀ j : η, ιs j → M}
     (hindep : ∀ j, LinearIndependent R (f j))
     (hd :
@@ -788,6 +881,7 @@ theorem linearIndependent_iUnion_finite {η : Type _} {ιs : η → Type _} {f :
   rw [range_sigma_eq_Union_range]
   apply linearIndependent_iUnion_finite_subtype (fun j => (hindep j).to_subtype_range) hd
 #align linear_independent_Union_finite linearIndependent_iUnion_finite
+-/
 
 end Subtype
 
@@ -795,6 +889,7 @@ section repr
 
 variable (hv : LinearIndependent R v)
 
+#print LinearIndependent.totalEquiv /-
 /-- Canonical isomorphism between linear combinations and the span of linearly independent vectors.
 -/
 @[simps (config := { rhsMd := semireducible })]
@@ -813,7 +908,9 @@ def LinearIndependent.totalEquiv (hv : LinearIndependent R v) : (ι →₀ R) 
     rw [LinearMap.mem_range]
     apply mem_range_self l
 #align linear_independent.total_equiv LinearIndependent.totalEquiv
+-/
 
+#print LinearIndependent.repr /-
 /-- Linear combination representing a vector in the span of linearly independent vectors.
 
 Given a family of linearly independent vectors, we can represent any vector in their span as
@@ -822,25 +919,35 @@ It is simply one direction of `linear_independent.total_equiv`. -/
 def LinearIndependent.repr (hv : LinearIndependent R v) : span R (range v) →ₗ[R] ι →₀ R :=
   hv.totalEquiv.symm
 #align linear_independent.repr LinearIndependent.repr
+-/
 
+#print LinearIndependent.total_repr /-
 @[simp]
 theorem LinearIndependent.total_repr (x) : Finsupp.total ι M R v (hv.repr x) = x :=
   Subtype.ext_iff.1 (LinearEquiv.apply_symm_apply hv.totalEquiv x)
 #align linear_independent.total_repr LinearIndependent.total_repr
+-/
 
+#print LinearIndependent.total_comp_repr /-
 theorem LinearIndependent.total_comp_repr :
     (Finsupp.total ι M R v).comp hv.repr = Submodule.subtype _ :=
   LinearMap.ext <| hv.total_repr
 #align linear_independent.total_comp_repr LinearIndependent.total_comp_repr
+-/
 
+#print LinearIndependent.repr_ker /-
 theorem LinearIndependent.repr_ker : hv.repr.ker = ⊥ := by
   rw [LinearIndependent.repr, LinearEquiv.ker]
 #align linear_independent.repr_ker LinearIndependent.repr_ker
+-/
 
+#print LinearIndependent.repr_range /-
 theorem LinearIndependent.repr_range : hv.repr.range = ⊤ := by
   rw [LinearIndependent.repr, LinearEquiv.range]
 #align linear_independent.repr_range LinearIndependent.repr_range
+-/
 
+#print LinearIndependent.repr_eq /-
 theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M R v l = ↑x) :
     hv.repr x = l :=
   by
@@ -856,13 +963,17 @@ theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M
   rw [← this]
   rfl
 #align linear_independent.repr_eq LinearIndependent.repr_eq
+-/
 
+#print LinearIndependent.repr_eq_single /-
 theorem LinearIndependent.repr_eq_single (i) (x) (hx : ↑x = v i) : hv.repr x = Finsupp.single i 1 :=
   by
   apply hv.repr_eq
   simp [Finsupp.total_single, hx]
 #align linear_independent.repr_eq_single LinearIndependent.repr_eq_single
+-/
 
+#print LinearIndependent.span_repr_eq /-
 theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
     Span.repr R (Set.range v) x = (hv.repr x).equivMapDomain (Equiv.ofInjective _ hv.Injective) :=
   by
@@ -877,7 +988,9 @@ theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
   ext ⟨_, ⟨i, rfl⟩⟩
   simp [← p]
 #align linear_independent.span_repr_eq LinearIndependent.span_repr_eq
+-/
 
+#print linearIndependent_iff_not_smul_mem_span /-
 -- TODO: why is this so slow?
 theorem linearIndependent_iff_not_smul_mem_span :
     LinearIndependent R v ↔ ∀ (i : ι) (a : R), a • v i ∈ span R (v '' (univ \ {i})) → a = 0 :=
@@ -900,7 +1013,9 @@ theorem linearIndependent_iff_not_smul_mem_span :
         simp [hij]
       · simp [hl]⟩
 #align linear_independent_iff_not_smul_mem_span linearIndependent_iff_not_smul_mem_span
+-/
 
+#print LinearIndependent.independent_span_singleton /-
 /-- See also `complete_lattice.independent_iff_linear_independent_of_ne_zero`. -/
 theorem LinearIndependent.independent_span_singleton (hv : LinearIndependent R v) :
     CompleteLattice.Independent fun i => R ∙ v i :=
@@ -916,9 +1031,11 @@ theorem LinearIndependent.independent_span_singleton (hv : LinearIndependent R v
   ext
   simp
 #align linear_independent.independent_span_singleton LinearIndependent.independent_span_singleton
+-/
 
 variable (R)
 
+#print exists_maximal_independent' /-
 theorem exists_maximal_independent' (s : ι → M) :
     ∃ I : Set ι,
       (LinearIndependent R fun x : I => s x) ∧
@@ -945,8 +1062,10 @@ theorem exists_maximal_independent' (s : ι → M) :
       (fun c hc => ⟨⟨⋃ I ∈ c, (I : Set ι), key c hc⟩, fun I => Set.subset_biUnion_of_mem⟩) trans
   exact ⟨I, hli, fun J hsub hli => Set.Subset.antisymm hsub (hmax ⟨J, hli⟩ hsub)⟩
 #align exists_maximal_independent' exists_maximal_independent'
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i «expr ∉ » I) -/
+#print exists_maximal_independent /-
 theorem exists_maximal_independent (s : ι → M) :
     ∃ I : Set ι,
       (LinearIndependent R fun x : I => s x) ∧
@@ -982,9 +1101,11 @@ theorem exists_maximal_independent (s : ι → M) :
   refine' neg_mem (sum_mem fun c hc => smul_mem _ _ (subset_span ⟨c, _, rfl⟩))
   exact (memJ.mp (supp_f (Finset.erase_subset _ _ hc))).resolve_left (Finset.ne_of_mem_erase hc)
 #align exists_maximal_independent exists_maximal_independent
+-/
 
 end repr
 
+#print surjective_of_linearIndependent_of_span /-
 theorem surjective_of_linearIndependent_of_span [Nontrivial R] (hv : LinearIndependent R v)
     (f : ι' ↪ ι) (hss : range v ⊆ span R (range (v ∘ f))) : Surjective f :=
   by
@@ -1007,7 +1128,9 @@ theorem surjective_of_linearIndependent_of_span [Nontrivial R] (hv : LinearIndep
   use i'
   exact hi'.2
 #align surjective_of_linear_independent_of_span surjective_of_linearIndependent_of_span
+-/
 
+#print eq_of_linearIndependent_of_span_subtype /-
 theorem eq_of_linearIndependent_of_span_subtype [Nontrivial R] {s t : Set M}
     (hs : LinearIndependent R (fun x => x : s → M)) (h : t ⊆ s) (hst : s ⊆ span R t) : s = t :=
   by
@@ -1025,9 +1148,11 @@ theorem eq_of_linearIndependent_of_span_subtype [Nontrivial R] {s t : Set M}
     rw [← Subtype.mk.inj hy]
     rfl
 #align eq_of_linear_independent_of_span_subtype eq_of_linearIndependent_of_span_subtype
+-/
 
 open LinearMap
 
+#print LinearIndependent.image_subtype /-
 theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
     (hs : LinearIndependent R (fun x => x : s → M)) (hf_inj : Disjoint (span R s) f.ker) :
     LinearIndependent R (fun x => x : f '' s → M') :=
@@ -1036,7 +1161,9 @@ theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
   refine' (hs.map hf_inj).to_subtype_range' _
   simp [Set.range_comp f]
 #align linear_independent.image_subtype LinearIndependent.image_subtype
+-/
 
+#print LinearIndependent.inl_union_inr /-
 theorem LinearIndependent.inl_union_inr {s : Set M} {t : Set M'}
     (hs : LinearIndependent R (fun x => x : s → M))
     (ht : LinearIndependent R (fun x => x : t → M')) :
@@ -1046,7 +1173,9 @@ theorem LinearIndependent.inl_union_inr {s : Set M} {t : Set M'}
   simp only [span_image]
   simp [disjoint_iff, prod_inf_prod]
 #align linear_independent.inl_union_inr LinearIndependent.inl_union_inr
+-/
 
+#print linearIndependent_inl_union_inr' /-
 theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv : LinearIndependent R v)
     (hv' : LinearIndependent R v') :
     LinearIndependent R (Sum.elim (inl R M M' ∘ v) (inr R M M' ∘ v')) :=
@@ -1054,7 +1183,9 @@ theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv :
     refine' is_compl_range_inl_inr.disjoint.mono _ _ <;>
       simp only [span_le, range_coe, range_comp_subset_range]
 #align linear_independent_inl_union_inr' linearIndependent_inl_union_inr'
+-/
 
+#print linearIndependent_monoidHom /-
 -- See, for example, Keith Conrad's note
 --  <https://kconrad.math.uconn.edu/blurbs/galoistheory/linearchar.pdf>
 /-- Dedekind's linear independence of characters -/
@@ -1143,7 +1274,9 @@ theorem linearIndependent_monoidHom (G : Type _) [Monoid G] (L : Type _) [CommRi
                 _ _ _).2
             ⟨h4, h3⟩
 #align linear_independent_monoid_hom linearIndependent_monoidHom
+-/
 
+#print le_of_span_le_span /-
 theorem le_of_span_le_span [Nontrivial R] {s t u : Set M} (hl : LinearIndependent R (coe : u → M))
     (hsu : s ⊆ u) (htu : t ⊆ u) (hst : span R s ≤ span R t) : s ⊆ t :=
   by
@@ -1152,11 +1285,14 @@ theorem le_of_span_le_span [Nontrivial R] {s t u : Set M} (hl : LinearIndependen
       (Set.subset_union_right _ _) (Set.union_subset (Set.Subset.trans subset_span hst) subset_span)
   rw [← this]; apply Set.subset_union_left
 #align le_of_span_le_span le_of_span_le_span
+-/
 
+#print span_le_span_iff /-
 theorem span_le_span_iff [Nontrivial R] {s t u : Set M} (hl : LinearIndependent R (coe : u → M))
     (hsu : s ⊆ u) (htu : t ⊆ u) : span R s ≤ span R t ↔ s ⊆ t :=
   ⟨le_of_span_le_span hl hsu htu, span_mono⟩
 #align span_le_span_iff span_le_span_iff
+-/
 
 end Module
 
@@ -1168,6 +1304,7 @@ variable [Module R M] [NoZeroSMulDivisors R M] [Module R M']
 
 variable {v : ι → M} {s t : Set M} {x y z : M}
 
+#print linearIndependent_unique_iff /-
 theorem linearIndependent_unique_iff (v : ι → M) [Unique ι] :
     LinearIndependent R v ↔ v default ≠ 0 :=
   by
@@ -1176,14 +1313,17 @@ theorem linearIndependent_unique_iff (v : ι → M) [Unique ι] :
   have := h (Finsupp.single default 1) (Or.inr hv)
   exact one_ne_zero (Finsupp.single_eq_zero.1 this)
 #align linear_independent_unique_iff linearIndependent_unique_iff
+-/
 
 alias linearIndependent_unique_iff ↔ _ linearIndependent_unique
 #align linear_independent_unique linearIndependent_unique
 
+#print linearIndependent_singleton /-
 theorem linearIndependent_singleton {x : M} (hx : x ≠ 0) :
     LinearIndependent R (fun x => x : ({x} : Set M) → M) :=
   linearIndependent_unique coe hx
 #align linear_independent_singleton linearIndependent_singleton
+-/
 
 end Nontrivial
 
@@ -1204,6 +1344,7 @@ variable {v : ι → V} {s t : Set V} {x y z : V}
 
 open Submodule
 
+#print mem_span_insert_exchange /-
 /- TODO: some of the following proofs can generalized with a zero_ne_one predicate type class
    (instead of a data containing type class) -/
 theorem mem_span_insert_exchange :
@@ -1215,7 +1356,9 @@ theorem mem_span_insert_exchange :
   have a0 : a ≠ 0 := by rintro rfl; simp_all
   simp [a0, smul_add, smul_smul]
 #align mem_span_insert_exchange mem_span_insert_exchange
+-/
 
+#print linearIndependent_iff_not_mem_span /-
 theorem linearIndependent_iff_not_mem_span :
     LinearIndependent K v ↔ ∀ i, v i ∉ span K (v '' (univ \ {i})) :=
   by
@@ -1227,7 +1370,9 @@ theorem linearIndependent_iff_not_mem_span :
     by_contra ha'
     exact False.elim (h _ ((smul_mem_iff _ ha').1 ha))
 #align linear_independent_iff_not_mem_span linearIndependent_iff_not_mem_span
+-/
 
+#print LinearIndependent.insert /-
 theorem LinearIndependent.insert (hs : LinearIndependent K (fun b => b : s → V))
     (hx : x ∉ span K s) : LinearIndependent K (fun b => b : insert x s → V) :=
   by
@@ -1236,7 +1381,9 @@ theorem LinearIndependent.insert (hs : LinearIndependent K (fun b => b : s → V
   apply hs.union (linearIndependent_singleton x0)
   rwa [disjoint_span_singleton' x0]
 #align linear_independent.insert LinearIndependent.insert
+-/
 
+#print linearIndependent_option' /-
 theorem linearIndependent_option' :
     LinearIndependent K (fun o => Option.casesOn' o x v : Option ι → V) ↔
       LinearIndependent K v ∧ x ∉ Submodule.span K (range v) :=
@@ -1248,19 +1395,25 @@ theorem linearIndependent_option' :
   rintro rfl
   exact h.2 (zero_mem _)
 #align linear_independent_option' linearIndependent_option'
+-/
 
+#print LinearIndependent.option /-
 theorem LinearIndependent.option (hv : LinearIndependent K v)
     (hx : x ∉ Submodule.span K (range v)) :
     LinearIndependent K (fun o => Option.casesOn' o x v : Option ι → V) :=
   linearIndependent_option'.2 ⟨hv, hx⟩
 #align linear_independent.option LinearIndependent.option
+-/
 
+#print linearIndependent_option /-
 theorem linearIndependent_option {v : Option ι → V} :
     LinearIndependent K v ↔
       LinearIndependent K (v ∘ coe : ι → V) ∧ v none ∉ Submodule.span K (range (v ∘ coe : ι → V)) :=
   by simp only [← linearIndependent_option', Option.casesOn'_none_coe]
 #align linear_independent_option linearIndependent_option
+-/
 
+#print linearIndependent_insert' /-
 theorem linearIndependent_insert' {ι} {s : Set ι} {a : ι} {f : ι → V} (has : a ∉ s) :
     (LinearIndependent K fun x : insert a s => f x) ↔
       (LinearIndependent K fun x : s => f x) ∧ f a ∉ Submodule.span K (f '' s) :=
@@ -1269,19 +1422,25 @@ theorem linearIndependent_insert' {ι} {s : Set ι} {a : ι} {f : ι → V} (has
     linearIndependent_option]
   simp [(· ∘ ·), range_comp f]
 #align linear_independent_insert' linearIndependent_insert'
+-/
 
+#print linearIndependent_insert /-
 theorem linearIndependent_insert (hxs : x ∉ s) :
     (LinearIndependent K fun b : insert x s => (b : V)) ↔
       (LinearIndependent K fun b : s => (b : V)) ∧ x ∉ Submodule.span K s :=
   (@linearIndependent_insert' _ _ _ _ _ _ _ _ id hxs).trans <| by simp
 #align linear_independent_insert linearIndependent_insert
+-/
 
+#print linearIndependent_pair /-
 theorem linearIndependent_pair {x y : V} (hx : x ≠ 0) (hy : ∀ a : K, a • x ≠ y) :
     LinearIndependent K (coe : ({x, y} : Set V) → V) :=
   pair_comm y x ▸ (linearIndependent_singleton hx).insert <|
     mt mem_span_singleton.1 (not_exists.2 hy)
 #align linear_independent_pair linearIndependent_pair
+-/
 
+#print linearIndependent_fin_cons /-
 theorem linearIndependent_fin_cons {n} {v : Fin n → V} :
     LinearIndependent K (Fin.cons x v : Fin (n + 1) → V) ↔
       LinearIndependent K v ∧ x ∉ Submodule.span K (range v) :=
@@ -1294,39 +1453,51 @@ theorem linearIndependent_fin_cons {n} {v : Fin n → V} :
   · ext
     rw [comp_app, comp_app, finSuccEquiv_symm_some, Fin.cons_succ]
 #align linear_independent_fin_cons linearIndependent_fin_cons
+-/
 
+#print linearIndependent_fin_snoc /-
 theorem linearIndependent_fin_snoc {n} {v : Fin n → V} :
     LinearIndependent K (Fin.snoc v x : Fin (n + 1) → V) ↔
       LinearIndependent K v ∧ x ∉ Submodule.span K (range v) :=
   by rw [Fin.snoc_eq_cons_rotate, linearIndependent_equiv, linearIndependent_fin_cons]
 #align linear_independent_fin_snoc linearIndependent_fin_snoc
+-/
 
+#print LinearIndependent.fin_cons /-
 /-- See `linear_independent.fin_cons'` for an uglier version that works if you
 only have a module over a semiring. -/
 theorem LinearIndependent.fin_cons {n} {v : Fin n → V} (hv : LinearIndependent K v)
     (hx : x ∉ Submodule.span K (range v)) : LinearIndependent K (Fin.cons x v : Fin (n + 1) → V) :=
   linearIndependent_fin_cons.2 ⟨hv, hx⟩
 #align linear_independent.fin_cons LinearIndependent.fin_cons
+-/
 
+#print linearIndependent_fin_succ /-
 theorem linearIndependent_fin_succ {n} {v : Fin (n + 1) → V} :
     LinearIndependent K v ↔
       LinearIndependent K (Fin.tail v) ∧ v 0 ∉ Submodule.span K (range <| Fin.tail v) :=
   by rw [← linearIndependent_fin_cons, Fin.cons_self_tail]
 #align linear_independent_fin_succ linearIndependent_fin_succ
+-/
 
+#print linearIndependent_fin_succ' /-
 theorem linearIndependent_fin_succ' {n} {v : Fin (n + 1) → V} :
     LinearIndependent K v ↔
       LinearIndependent K (Fin.init v) ∧ v (Fin.last _) ∉ Submodule.span K (range <| Fin.init v) :=
   by rw [← linearIndependent_fin_snoc, Fin.snoc_init_self]
 #align linear_independent_fin_succ' linearIndependent_fin_succ'
+-/
 
+#print linearIndependent_fin2 /-
 theorem linearIndependent_fin2 {f : Fin 2 → V} :
     LinearIndependent K f ↔ f 1 ≠ 0 ∧ ∀ a : K, a • f 1 ≠ f 0 := by
   rw [linearIndependent_fin_succ, linearIndependent_unique_iff, range_unique, mem_span_singleton,
     not_exists, show Fin.tail f default = f 1 by rw [← Fin.succ_zero_eq_one] <;> rfl]
 #align linear_independent_fin2 linearIndependent_fin2
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (b «expr ⊆ » t) -/
+#print exists_linearIndependent_extension /-
 theorem exists_linearIndependent_extension (hs : LinearIndependent K (coe : s → V)) (hst : s ⊆ t) :
     ∃ (b : _) (_ : b ⊆ t), s ⊆ b ∧ t ⊆ span K b ∧ LinearIndependent K (coe : b → V) :=
   by
@@ -1342,10 +1513,12 @@ theorem exists_linearIndependent_extension (hs : LinearIndependent K (coe : s 
     · exact linearIndependent_sUnion_of_directed cc.directed_on fun x xc => (hc xc).2
     · exact subset_sUnion_of_mem
 #align exists_linear_independent_extension exists_linearIndependent_extension
+-/
 
 variable (K t)
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (b «expr ⊆ » t) -/
+#print exists_linearIndependent /-
 theorem exists_linearIndependent :
     ∃ (b : _) (_ : b ⊆ t), span K b = span K t ∧ LinearIndependent K (coe : b → V) :=
   by
@@ -1353,6 +1526,7 @@ theorem exists_linearIndependent :
     exists_linearIndependent_extension (linearIndependent_empty K V) (Set.empty_subset t)
   exact ⟨b, hb₁, (span_eq_of_le _ hb₂ (Submodule.span_mono hb₁)).symm, hb₃⟩
 #align exists_linear_independent exists_linearIndependent
+-/
 
 variable {K t}
 
@@ -1365,32 +1539,41 @@ noncomputable def LinearIndependent.extend (hs : LinearIndependent K (fun x => x
 #align linear_independent.extend LinearIndependent.extend
 -/
 
+#print LinearIndependent.extend_subset /-
 theorem LinearIndependent.extend_subset (hs : LinearIndependent K (fun x => x : s → V))
     (hst : s ⊆ t) : hs.extend hst ⊆ t :=
   let ⟨hbt, hsb, htb, hli⟩ := Classical.choose_spec (exists_linearIndependent_extension hs hst)
   hbt
 #align linear_independent.extend_subset LinearIndependent.extend_subset
+-/
 
+#print LinearIndependent.subset_extend /-
 theorem LinearIndependent.subset_extend (hs : LinearIndependent K (fun x => x : s → V))
     (hst : s ⊆ t) : s ⊆ hs.extend hst :=
   let ⟨hbt, hsb, htb, hli⟩ := Classical.choose_spec (exists_linearIndependent_extension hs hst)
   hsb
 #align linear_independent.subset_extend LinearIndependent.subset_extend
+-/
 
+#print LinearIndependent.subset_span_extend /-
 theorem LinearIndependent.subset_span_extend (hs : LinearIndependent K (fun x => x : s → V))
     (hst : s ⊆ t) : t ⊆ span K (hs.extend hst) :=
   let ⟨hbt, hsb, htb, hli⟩ := Classical.choose_spec (exists_linearIndependent_extension hs hst)
   htb
 #align linear_independent.subset_span_extend LinearIndependent.subset_span_extend
+-/
 
+#print LinearIndependent.linearIndependent_extend /-
 theorem LinearIndependent.linearIndependent_extend (hs : LinearIndependent K (fun x => x : s → V))
     (hst : s ⊆ t) : LinearIndependent K (coe : hs.extend hst → V) :=
   let ⟨hbt, hsb, htb, hli⟩ := Classical.choose_spec (exists_linearIndependent_extension hs hst)
   hli
 #align linear_independent.linear_independent_extend LinearIndependent.linearIndependent_extend
+-/
 
 variable {K V}
 
+#print exists_of_linearIndependent_of_finite_span /-
 -- TODO(Mario): rewrite?
 theorem exists_of_linearIndependent_of_finite_span {t : Finset V}
     (hs : LinearIndependent K (fun x => x : s → V)) (hst : s ⊆ (span K ↑t : Submodule K V)) :
@@ -1453,7 +1636,9 @@ theorem exists_of_linearIndependent_of_finite_span {t : Finset V}
     ⟨u, subset.trans h.1 (by simp (config := { contextual := true }) [subset_def, and_imp, or_imp]),
       h.2.1, by simp only [h.2.2, Eq]⟩
 #align exists_of_linear_independent_of_finite_span exists_of_linearIndependent_of_finite_span
+-/
 
+#print exists_finite_card_le_of_finite_of_linearIndependent_of_span /-
 theorem exists_finite_card_le_of_finite_of_linearIndependent_of_span (ht : t.Finite)
     (hs : LinearIndependent K (fun x => x : s → V)) (hst : s ⊆ span K t) :
     ∃ h : s.Finite, h.toFinset.card ≤ ht.toFinset.card :=
@@ -1462,6 +1647,7 @@ theorem exists_finite_card_le_of_finite_of_linearIndependent_of_span (ht : t.Fin
   have : s.Finite := u.finite_toSet.Subset hsu
   ⟨this, by rw [← Eq] <;> exact Finset.card_le_of_subset <| finset.coe_subset.mp <| by simp [hsu]⟩
 #align exists_finite_card_le_of_finite_of_linear_independent_of_span exists_finite_card_le_of_finite_of_linearIndependent_of_span
+-/
 
 end Module

bump to nightly-2023-06-10-07

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

3fdc57bc

Diff

@@ -118,7 +118,7 @@ theorem linearIndependent_iff : LinearIndependent R v ↔ ∀ l, Finsupp.total 
 
 theorem linearIndependent_iff' :
     LinearIndependent R v ↔
-      ∀ s : Finset ι, ∀ g : ι → R, (∑ i in s, g i • v i) = 0 → ∀ i ∈ s, g i = 0 :=
+      ∀ s : Finset ι, ∀ g : ι → R, ∑ i in s, g i • v i = 0 → ∀ i ∈ s, g i = 0 :=
   linearIndependent_iff.trans
     ⟨fun hf s g hg i his =>
       have h :=
@@ -144,7 +144,7 @@ theorem linearIndependent_iff' :
 theorem linearIndependent_iff'' :
     LinearIndependent R v ↔
       ∀ (s : Finset ι) (g : ι → R) (hg : ∀ (i) (_ : i ∉ s), g i = 0),
-        (∑ i in s, g i • v i) = 0 → ∀ i, g i = 0 :=
+        ∑ i in s, g i • v i = 0 → ∀ i, g i = 0 :=
   linearIndependent_iff'.trans
     ⟨fun H s g hg hv i => if his : i ∈ s then H s g hv i his else hg i his, fun H s g hg i hi =>
       by
@@ -156,14 +156,14 @@ theorem linearIndependent_iff'' :
 
 theorem not_linearIndependent_iff :
     ¬LinearIndependent R v ↔
-      ∃ s : Finset ι, ∃ g : ι → R, (∑ i in s, g i • v i) = 0 ∧ ∃ i ∈ s, g i ≠ 0 :=
+      ∃ s : Finset ι, ∃ g : ι → R, ∑ i in s, g i • v i = 0 ∧ ∃ i ∈ s, g i ≠ 0 :=
   by
   rw [linearIndependent_iff']
   simp only [exists_prop, not_forall]
 #align not_linear_independent_iff not_linearIndependent_iff
 
 theorem Fintype.linearIndependent_iff [Fintype ι] :
-    LinearIndependent R v ↔ ∀ g : ι → R, (∑ i, g i • v i) = 0 → ∀ i, g i = 0 :=
+    LinearIndependent R v ↔ ∀ g : ι → R, ∑ i, g i • v i = 0 → ∀ i, g i = 0 :=
   by
   refine'
     ⟨fun H g => by simpa using linearIndependent_iff'.1 H Finset.univ g, fun H =>
@@ -182,7 +182,7 @@ theorem Fintype.linearIndependent_iff' [Fintype ι] :
 #align fintype.linear_independent_iff' Fintype.linearIndependent_iff'
 
 theorem Fintype.not_linearIndependent_iff [Fintype ι] :
-    ¬LinearIndependent R v ↔ ∃ g : ι → R, (∑ i, g i • v i) = 0 ∧ ∃ i, g i ≠ 0 := by
+    ¬LinearIndependent R v ↔ ∃ g : ι → R, ∑ i, g i • v i = 0 ∧ ∃ i, g i ≠ 0 := by
   simpa using not_iff_not.2 Fintype.linearIndependent_iff
 #align fintype.not_linear_independent_iff Fintype.not_linearIndependent_iff
 
@@ -248,8 +248,7 @@ the original family. -/
 theorem LinearIndependent.of_comp (f : M →ₗ[R] M') (hfv : LinearIndependent R (f ∘ v)) :
     LinearIndependent R v :=
   linearIndependent_iff'.2 fun s g hg i his =>
-    have : (∑ i : ι in s, g i • f (v i)) = 0 := by
-      simp_rw [← f.map_smul, ← f.map_sum, hg, f.map_zero]
+    have : ∑ i : ι in s, g i • f (v i) = 0 := by simp_rw [← f.map_smul, ← f.map_sum, hg, f.map_zero]
     linearIndependent_iff'.1 hfv s g this i his
 #align linear_independent.of_comp LinearIndependent.of_comp
 
@@ -398,7 +397,7 @@ theorem linearDependent_comp_subtype' {s : Set ι} :
 /-- A version of `linear_dependent_comp_subtype'` with `finsupp.total` unfolded. -/
 theorem linearDependent_comp_subtype {s : Set ι} :
     ¬LinearIndependent R (v ∘ coe : s → M) ↔
-      ∃ f : ι →₀ R, f ∈ Finsupp.supported R R s ∧ (∑ i in f.support, f i • v i) = 0 ∧ f ≠ 0 :=
+      ∃ f : ι →₀ R, f ∈ Finsupp.supported R R s ∧ ∑ i in f.support, f i • v i = 0 ∧ f ≠ 0 :=
   linearDependent_comp_subtype'
 #align linear_dependent_comp_subtype linearDependent_comp_subtype
 
@@ -710,8 +709,8 @@ theorem linearIndependent_sum {v : Sum ι ι' → M} :
   rw [linearIndependent_iff'] at *
   intro s g hg i hi
   have :
-    ((∑ i in s.preimage Sum.inl (sum.inl_injective.inj_on _), (fun x => g x • v x) (Sum.inl i)) +
-        ∑ i in s.preimage Sum.inr (sum.inr_injective.inj_on _), (fun x => g x • v x) (Sum.inr i)) =
+    ∑ i in s.preimage Sum.inl (sum.inl_injective.inj_on _), (fun x => g x • v x) (Sum.inl i) +
+        ∑ i in s.preimage Sum.inr (sum.inr_injective.inj_on _), (fun x => g x • v x) (Sum.inr i) =
       0 :=
     by
     rw [Finset.sum_preimage', Finset.sum_preimage', ← Finset.sum_union, ← Finset.filter_or]
@@ -1089,20 +1088,18 @@ theorem linearIndependent_monoidHom (G : Type _) [Monoid G] (L : Type _) [CommRi
                             y =
                           ∑ i in s, (g i * i x - g i * a x) * i y :=
                         Finset.sum_apply _ _ _
-                      _ = ∑ i in s, g i * i x * i y - g i * a x * i y :=
+                      _ = ∑ i in s, (g i * i x * i y - g i * a x * i y) :=
                         (Finset.sum_congr rfl fun _ _ => sub_mul _ _ _)
-                      _ = (∑ i in s, g i * i x * i y) - ∑ i in s, g i * a x * i y :=
+                      _ = ∑ i in s, g i * i x * i y - ∑ i in s, g i * a x * i y :=
                         Finset.sum_sub_distrib
                       _ =
-                          (g a * a x * a y + ∑ i in s, g i * i x * i y) -
+                          g a * a x * a y + ∑ i in s, g i * i x * i y -
                             (g a * a x * a y + ∑ i in s, g i * a x * i y) :=
                         by rw [add_sub_add_left_eq_sub]
-                      _ =
-                          (∑ i in insert a s, g i * i x * i y) -
-                            ∑ i in insert a s, g i * a x * i y :=
+                      _ = ∑ i in insert a s, g i * i x * i y - ∑ i in insert a s, g i * a x * i y :=
                         by rw [Finset.sum_insert has, Finset.sum_insert has]
                       _ =
-                          (∑ i in insert a s, g i * i (x * y)) -
+                          ∑ i in insert a s, g i * i (x * y) -
                             ∑ i in insert a s, a x * (g i * i y) :=
                         (congr
                           (congr_arg Sub.sub

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -134,8 +134,7 @@ theorem linearIndependent_iff' :
               fun hnis => hnis.elim his)
         _ = (∑ j in s, Finsupp.single j (g j)) i :=
           (Finsupp.lapply i : (ι →₀ R) →ₗ[R] R).map_sum.symm
-        _ = 0 := Finsupp.ext_iff.1 h i
-        ,
+        _ = 0 := Finsupp.ext_iff.1 h i,
       fun hf l hl =>
       Finsupp.ext fun i =>
         by_contradiction fun hni => hni <| hf _ _ hl _ <| Finsupp.mem_support_iff.2 hni⟩
@@ -1114,8 +1113,7 @@ theorem linearIndependent_monoidHom (G : Type _) [Monoid G] (L : Type _) [CommRi
                             a x * (∑ i in insert a s, (g i • i : G → L)) y :=
                         by rw [Finset.sum_apply, Finset.sum_apply, Finset.mul_sum] <;> rfl
                       _ = 0 - a x * 0 := by rw [hg] <;> rfl
-                      _ = 0 := by rw [MulZeroClass.mul_zero, sub_zero]
-                      )
+                      _ = 0 := by rw [MulZeroClass.mul_zero, sub_zero])
                   i his
           -- On the other hand, since `a` is not already in `s`, for any character `i ∈ s`
           -- there is some element of the monoid on which it differs from `a`.
@@ -1142,7 +1140,6 @@ theorem linearIndependent_monoidHom (G : Type _) [Monoid G] (L : Type _) [CommRi
                   rw [h3 i (his.resolve_left hia), zero_smul]
                 · intro haas; exfalso; apply haas; exact Finset.mem_insert_self a s
               _ = 0 := by rw [hg] <;> rfl
-              
           (-- Now we're done; the last two facts together imply that `g` vanishes on every element
                 -- of `insert a s`.
                 Finset.forall_mem_insert

bump to nightly-2023-06-08-23

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

d3cfe2e3

Diff

@@ -141,7 +141,7 @@ theorem linearIndependent_iff' :
         by_contradiction fun hni => hni <| hf _ _ hl _ <| Finsupp.mem_support_iff.2 hni⟩
 #align linear_independent_iff' linearIndependent_iff'
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i «expr ∉ » s) -/
 theorem linearIndependent_iff'' :
     LinearIndependent R v ↔
       ∀ (s : Finset ι) (g : ι → R) (hg : ∀ (i) (_ : i ∉ s), g i = 0),
@@ -452,7 +452,7 @@ theorem LinearIndependent.mono {t s : Set M} (h : t ⊆ s) :
 #align linear_independent.mono LinearIndependent.mono
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print linearIndependent_of_finite /-
 theorem linearIndependent_of_finite (s : Set M)
     (H : ∀ (t) (_ : t ⊆ s), Set.Finite t → LinearIndependent R (fun x => x : t → M)) :
@@ -948,7 +948,7 @@ theorem exists_maximal_independent' (s : ι → M) :
   exact ⟨I, hli, fun J hsub hli => Set.Subset.antisymm hsub (hmax ⟨J, hli⟩ hsub)⟩
 #align exists_maximal_independent' exists_maximal_independent'
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » I) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i «expr ∉ » I) -/
 theorem exists_maximal_independent (s : ι → M) :
     ∃ I : Set ι,
       (LinearIndependent R fun x : I => s x) ∧
@@ -1332,7 +1332,7 @@ theorem linearIndependent_fin2 {f : Fin 2 → V} :
     not_exists, show Fin.tail f default = f 1 by rw [← Fin.succ_zero_eq_one] <;> rfl]
 #align linear_independent_fin2 linearIndependent_fin2
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (b «expr ⊆ » t) -/
 theorem exists_linearIndependent_extension (hs : LinearIndependent K (coe : s → V)) (hst : s ⊆ t) :
     ∃ (b : _) (_ : b ⊆ t), s ⊆ b ∧ t ⊆ span K b ∧ LinearIndependent K (coe : b → V) :=
   by
@@ -1351,7 +1351,7 @@ theorem exists_linearIndependent_extension (hs : LinearIndependent K (coe : s 
 
 variable (K t)
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (b «expr ⊆ » t) -/
 theorem exists_linearIndependent :
     ∃ (b : _) (_ : b ⊆ t), span K b = span K t ∧ LinearIndependent K (coe : b → V) :=
   by

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -149,7 +149,8 @@ theorem linearIndependent_iff'' :
   linearIndependent_iff'.trans
     ⟨fun H s g hg hv i => if his : i ∈ s then H s g hv i his else hg i his, fun H s g hg i hi =>
       by
-      convert H s (fun j => if j ∈ s then g j else 0) (fun j hj => if_neg hj)
+      convert
+        H s (fun j => if j ∈ s then g j else 0) (fun j hj => if_neg hj)
           (by simp_rw [ite_smul, zero_smul, Finset.sum_extend_by_zero, hg]) i
       exact (if_pos hi).symm⟩
 #align linear_independent_iff'' linearIndependent_iff''
@@ -954,34 +955,34 @@ theorem exists_maximal_independent (s : ι → M) :
         ∀ (i) (_ : i ∉ I), ∃ a : R, a ≠ 0 ∧ a • s i ∈ span R (s '' I) :=
   by
   classical
-    rcases exists_maximal_independent' R s with ⟨I, hIlinind, hImaximal⟩
-    use I, hIlinind
-    intro i hi
-    specialize hImaximal (I ∪ {i}) (by simp)
-    set J := I ∪ {i} with hJ
-    have memJ : ∀ {x}, x ∈ J ↔ x = i ∨ x ∈ I := by simp [hJ]
-    have hiJ : i ∈ J := by simp
-    have h := mt hImaximal _
-    swap
-    · intro h2
-      rw [h2] at hi 
-      exact absurd hiJ hi
-    obtain ⟨f, supp_f, sum_f, f_ne⟩ := linear_dependent_comp_subtype.mp h
-    have hfi : f i ≠ 0 := by
-      contrapose hIlinind
-      refine' linear_dependent_comp_subtype.mpr ⟨f, _, sum_f, f_ne⟩
-      simp only [Finsupp.mem_supported, hJ] at supp_f ⊢
-      rintro x hx
-      refine' (memJ.mp (supp_f hx)).resolve_left _
-      rintro rfl
-      exact hIlinind (finsupp.mem_support_iff.mp hx)
-    use f i, hfi
-    have hfi' : i ∈ f.support := finsupp.mem_support_iff.mpr hfi
-    rw [← Finset.insert_erase hfi', Finset.sum_insert (Finset.not_mem_erase _ _),
-      add_eq_zero_iff_eq_neg] at sum_f 
-    rw [sum_f]
-    refine' neg_mem (sum_mem fun c hc => smul_mem _ _ (subset_span ⟨c, _, rfl⟩))
-    exact (memJ.mp (supp_f (Finset.erase_subset _ _ hc))).resolve_left (Finset.ne_of_mem_erase hc)
+  rcases exists_maximal_independent' R s with ⟨I, hIlinind, hImaximal⟩
+  use I, hIlinind
+  intro i hi
+  specialize hImaximal (I ∪ {i}) (by simp)
+  set J := I ∪ {i} with hJ
+  have memJ : ∀ {x}, x ∈ J ↔ x = i ∨ x ∈ I := by simp [hJ]
+  have hiJ : i ∈ J := by simp
+  have h := mt hImaximal _
+  swap
+  · intro h2
+    rw [h2] at hi 
+    exact absurd hiJ hi
+  obtain ⟨f, supp_f, sum_f, f_ne⟩ := linear_dependent_comp_subtype.mp h
+  have hfi : f i ≠ 0 := by
+    contrapose hIlinind
+    refine' linear_dependent_comp_subtype.mpr ⟨f, _, sum_f, f_ne⟩
+    simp only [Finsupp.mem_supported, hJ] at supp_f ⊢
+    rintro x hx
+    refine' (memJ.mp (supp_f hx)).resolve_left _
+    rintro rfl
+    exact hIlinind (finsupp.mem_support_iff.mp hx)
+  use f i, hfi
+  have hfi' : i ∈ f.support := finsupp.mem_support_iff.mpr hfi
+  rw [← Finset.insert_erase hfi', Finset.sum_insert (Finset.not_mem_erase _ _),
+    add_eq_zero_iff_eq_neg] at sum_f 
+  rw [sum_f]
+  refine' neg_mem (sum_mem fun c hc => smul_mem _ _ (subset_span ⟨c, _, rfl⟩))
+  exact (memJ.mp (supp_f (Finset.erase_subset _ _ hc))).resolve_left (Finset.ne_of_mem_erase hc)
 #align exists_maximal_independent exists_maximal_independent
 
 end repr
@@ -1335,7 +1336,7 @@ theorem linearIndependent_fin2 {f : Fin 2 → V} :
 theorem exists_linearIndependent_extension (hs : LinearIndependent K (coe : s → V)) (hst : s ⊆ t) :
     ∃ (b : _) (_ : b ⊆ t), s ⊆ b ∧ t ⊆ span K b ∧ LinearIndependent K (coe : b → V) :=
   by
-  rcases zorn_subset_nonempty { b | b ⊆ t ∧ LinearIndependent K (coe : b → V) } _ _ ⟨hst, hs⟩ with
+  rcases zorn_subset_nonempty {b | b ⊆ t ∧ LinearIndependent K (coe : b → V)} _ _ ⟨hst, hs⟩ with
     ⟨b, ⟨bt, bi⟩, sb, h⟩
   · refine' ⟨b, bt, sb, fun x xt => _, bi⟩
     by_contra hn

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -227,9 +227,9 @@ theorem LinearIndependent.map (hv : LinearIndependent R v) {f : M →ₗ[R] M'}
   by
   rw [disjoint_iff_inf_le, ← Set.image_univ, Finsupp.span_image_eq_map_total,
     map_inf_eq_map_inf_comap, map_le_iff_le_comap, comap_bot, Finsupp.supported_univ, top_inf_eq] at
-    hf_inj
-  unfold LinearIndependent at hv⊢
-  rw [hv, le_bot_iff] at hf_inj
+    hf_inj 
+  unfold LinearIndependent at hv ⊢
+  rw [hv, le_bot_iff] at hf_inj 
   haveI : Inhabited M := ⟨0⟩
   rw [Finsupp.total_comp, @Finsupp.lmapDomain_total _ _ R _ _ _ _ _ _ _ _ _ _ f, LinearMap.ker_comp,
     hf_inj]
@@ -304,14 +304,14 @@ theorem LinearIndependent.fin_cons' {m : ℕ} (x : M) (v : Fin m → M) (hli : L
     (x_ortho : ∀ (c : R) (y : Submodule.span R (Set.range v)), c • x + y = (0 : M) → c = 0) :
     LinearIndependent R (Fin.cons x v : Fin m.succ → M) :=
   by
-  rw [Fintype.linearIndependent_iff] at hli⊢
+  rw [Fintype.linearIndependent_iff] at hli ⊢
   rintro g total_eq j
-  simp_rw [Fin.sum_univ_succ, Fin.cons_zero, Fin.cons_succ] at total_eq
+  simp_rw [Fin.sum_univ_succ, Fin.cons_zero, Fin.cons_succ] at total_eq 
   have : g 0 = 0 :=
     by
     refine' x_ortho (g 0) ⟨∑ i : Fin m, g i.succ • v i, _⟩ total_eq
     exact sum_mem fun i _ => smul_mem _ _ (subset_span ⟨i, rfl⟩)
-  rw [this, zero_smul, zero_add] at total_eq
+  rw [this, zero_smul, zero_add] at total_eq 
   exact Fin.cases this (hli _ total_eq) j
 #align linear_independent.fin_cons' LinearIndependent.fin_cons'
 
@@ -339,12 +339,12 @@ theorem linearIndependent_finset_map_embedding_subtype (s : Set M)
   let f : t.map (embedding.subtype s) → s := fun x =>
     ⟨x.1, by
       obtain ⟨x, h⟩ := x
-      rw [Finset.mem_map] at h
+      rw [Finset.mem_map] at h 
       obtain ⟨a, ha, rfl⟩ := h
       simp only [Subtype.coe_prop, embedding.coe_subtype]⟩
   convert LinearIndependent.comp li f _
   rintro ⟨x, hx⟩ ⟨y, hy⟩
-  rw [Finset.mem_map] at hx hy
+  rw [Finset.mem_map] at hx hy 
   obtain ⟨a, ha, rfl⟩ := hx
   obtain ⟨b, hb, rfl⟩ := hy
   simp only [imp_self, Subtype.mk_eq_mk]
@@ -384,9 +384,9 @@ theorem linearIndependent_comp_subtype {s : Set ι} :
   · intro h l hl
     refine' Finsupp.embDomain_eq_zero.1 (h (l.emb_domain <| Function.Embedding.subtype s) _ _)
     · suffices ∀ i hi, ¬l ⟨i, hi⟩ = 0 → i ∈ s by simpa
-      intros ; assumption
+      intros; assumption
     · rwa [Finsupp.embDomain_eq_mapDomain, Finsupp.sum_mapDomain_index]
-      exacts[fun _ => zero_smul _ _, fun _ _ _ => add_smul _ _ _]
+      exacts [fun _ => zero_smul _ _, fun _ _ _ => add_smul _ _ _]
 #align linear_independent_comp_subtype linearIndependent_comp_subtype
 
 theorem linearDependent_comp_subtype' {s : Set ι} :
@@ -532,7 +532,7 @@ theorem LinearIndependent.injective [Nontrivial R] (hv : LinearIndependent R v)
     simp [hij]
   have h_single_eq : Finsupp.single i (1 : R) = Finsupp.single j 1 :=
     by
-    rw [linearIndependent_iff] at hv
+    rw [linearIndependent_iff] at hv 
     simp [eq_add_of_sub_eq' (hv l h_total)]
   simpa [Finsupp.single_eq_single_iff] using h_single_eq
 #align linear_independent.injective LinearIndependent.injective
@@ -566,14 +566,14 @@ theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulActi
     [DistribMulAction G M] [IsScalarTower G R M] [SMulCommClass G R M] {v : ι → M}
     (hv : LinearIndependent R v) (w : ι → G) : LinearIndependent R (w • v) :=
   by
-  rw [linearIndependent_iff''] at hv⊢
+  rw [linearIndependent_iff''] at hv ⊢
   intro s g hgs hsum i
   refine' (smul_eq_zero_iff_eq (w i)).1 _
   refine' hv s (fun i => w i • g i) (fun i hi => _) _ i
   · dsimp only
     exact (hgs i hi).symm ▸ smul_zero _
   · rw [← hsum, Finset.sum_congr rfl _]
-    intros ; erw [Pi.smul_apply, smul_assoc, smul_comm]
+    intros; erw [Pi.smul_apply, smul_assoc, smul_comm]
 #align linear_independent.group_smul LinearIndependent.group_smul
 
 -- This lemma cannot be proved with `linear_independent.group_smul` since the action of
@@ -581,7 +581,7 @@ theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulActi
 theorem LinearIndependent.units_smul {v : ι → M} (hv : LinearIndependent R v) (w : ι → Rˣ) :
     LinearIndependent R (w • v) :=
   by
-  rw [linearIndependent_iff''] at hv⊢
+  rw [linearIndependent_iff''] at hv ⊢
   intro s g hgs hsum i
   rw [← (w i).mul_left_eq_zero]
   refine' hv s (fun i => g i • w i) (fun i hi => _) _ i
@@ -621,13 +621,13 @@ theorem LinearIndependent.maximal_iff {ι : Type w} {R : Type u} [Ring R] [Nontr
   fconstructor
   · rintro p κ w i' j rfl
     specialize p (range w) i'.coe_range (range_comp_subset_range _ _)
-    rw [range_comp, ← @image_univ _ _ w] at p
+    rw [range_comp, ← @image_univ _ _ w] at p 
     exact range_iff_surjective.mp (image_injective.mpr i'.injective p)
   · intro p w i' h
     specialize p w (coe : w → M) i' (fun i => ⟨v i, range_subset_iff.mp h i⟩) (by ext; simp)
     have q := congr_arg (fun s => (coe : w → M) '' s) p.range_eq
-    dsimp at q
-    rw [← image_univ, image_image] at q
+    dsimp at q 
+    rw [← image_univ, image_image] at q 
     simpa using q
 #align linear_independent.maximal_iff LinearIndependent.maximal_iff
 -/
@@ -646,7 +646,7 @@ theorem LinearIndependent.eq_of_smul_apply_eq_smul_apply {M : Type _} [AddCommGr
     simp [h]
   have h_single_eq : Finsupp.single i c = Finsupp.single j d :=
     by
-    rw [linearIndependent_iff] at li
+    rw [linearIndependent_iff] at li 
     simp [eq_add_of_sub_eq' (li l h_total)]
   rcases(Finsupp.single_eq_single_iff _ _ _ _).mp h_single_eq with (⟨this, _⟩ | ⟨hc, _⟩)
   · exact this
@@ -663,7 +663,7 @@ theorem LinearIndependent.disjoint_span_image (hv : LinearIndependent R v) {s t
   by
   simp only [disjoint_def, Finsupp.mem_span_image_iff_total]
   rintro _ ⟨l₁, hl₁, rfl⟩ ⟨l₂, hl₂, H⟩
-  rw [hv.injective_total.eq_iff] at H; subst l₂
+  rw [hv.injective_total.eq_iff] at H ; subst l₂
   have : l₁ = 0 := submodule.disjoint_def.mp (Finsupp.disjoint_supported_supported hs) _ hl₁ hl₂
   simp [this]
 #align linear_independent.disjoint_span_image LinearIndependent.disjoint_span_image
@@ -687,9 +687,9 @@ theorem LinearIndependent.total_ne_of_not_mem_support [Nontrivial R] (hv : Linea
   replace h : x ∉ (f.support : Set ι) := h
   have p := hv.not_mem_span_image h
   intro w
-  rw [← w] at p
-  rw [Finsupp.span_image_eq_map_total] at p
-  simp only [not_exists, not_and, mem_map] at p
+  rw [← w] at p 
+  rw [Finsupp.span_image_eq_map_total] at p 
+  simp only [not_exists, not_and, mem_map] at p 
   exact p f (f.mem_supported_support R) rfl
 #align linear_independent.total_ne_of_not_mem_support LinearIndependent.total_ne_of_not_mem_support
 
@@ -717,12 +717,12 @@ theorem linearIndependent_sum {v : Sum ι ι' → M} :
     rw [Finset.sum_preimage', Finset.sum_preimage', ← Finset.sum_union, ← Finset.filter_or]
     · simpa only [← mem_union, range_inl_union_range_inr, mem_univ, Finset.filter_True]
     · exact Finset.disjoint_filter.2 fun x _ hx => disjoint_left.1 is_compl_range_inl_range_inr.1 hx
-  · rw [← eq_neg_iff_add_eq_zero] at this
-    rw [disjoint_def'] at hlr
+  · rw [← eq_neg_iff_add_eq_zero] at this 
+    rw [disjoint_def'] at hlr 
     have A := hlr _ (sum_mem fun i hi => _) _ (neg_mem <| sum_mem fun i hi => _) this
     · cases' i with i i
       · exact hl _ _ A i (Finset.mem_preimage.2 hi)
-      · rw [this, neg_eq_zero] at A
+      · rw [this, neg_eq_zero] at A 
         exact hr _ _ A i (Finset.mem_preimage.2 hi)
     · exact smul_mem _ _ (subset_span ⟨Sum.inl i, mem_range_self _, rfl⟩)
     · exact smul_mem _ _ (subset_span ⟨Sum.inr i, mem_range_self _, rfl⟩)
@@ -766,7 +766,7 @@ theorem linearIndependent_iUnion_finite {η : Type _} {ιs : η → Type _} {f :
       ∀ i,
         ∀ t : Set η,
           t.Finite → i ∉ t → Disjoint (span R (range (f i))) (⨆ i ∈ t, span R (range (f i)))) :
-    LinearIndependent R fun ji : Σj, ιs j => f ji.1 ji.2 :=
+    LinearIndependent R fun ji : Σ j, ιs j => f ji.1 ji.2 :=
   by
   nontriviality R
   apply LinearIndependent.of_subtype_range
@@ -782,7 +782,7 @@ theorem linearIndependent_iUnion_finite {η : Type _} {ιs : η → Type _} {f :
           disjoint_def.1 (hd x₁ {y₁} (finite_singleton y₁) fun h => h_cases (eq_of_mem_singleton h))
             (f x₁ x₂) (subset_span (mem_range_self _))
         rw [iSup_singleton]
-        simp only at hxy
+        simp only at hxy 
         rw [hxy]
         exact subset_span (mem_range_self y₂)
       exact False.elim ((hindep x₁).NeZero _ h0)
@@ -851,7 +851,7 @@ theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M
     rfl
   have : (LinearIndependent.totalEquiv hv : (ι →₀ R) →ₗ[R] span R (range v)) l = x :=
     by
-    rw [Eq] at this
+    rw [Eq] at this 
     exact Subtype.ext_iff.2 this
   rw [← LinearEquiv.symm_apply_apply hv.total_equiv l]
   rw [← this]
@@ -883,9 +883,9 @@ theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
 theorem linearIndependent_iff_not_smul_mem_span :
     LinearIndependent R v ↔ ∀ (i : ι) (a : R), a • v i ∈ span R (v '' (univ \ {i})) → a = 0 :=
   ⟨fun hv i a ha => by
-    rw [Finsupp.span_image_eq_map_total, mem_map] at ha
+    rw [Finsupp.span_image_eq_map_total, mem_map] at ha 
     rcases ha with ⟨l, hl, e⟩
-    rw [sub_eq_zero.1 (linearIndependent_iff.1 hv (l - Finsupp.single i a) (by simp [e]))] at hl
+    rw [sub_eq_zero.1 (linearIndependent_iff.1 hv (l - Finsupp.single i a) (by simp [e]))] at hl 
     by_contra hn
     exact (not_mem_of_mem_diff (hl <| by simp [hn])) (mem_singleton _), fun H =>
     linearIndependent_iff.2 fun l hl => by
@@ -909,7 +909,7 @@ theorem LinearIndependent.independent_span_singleton (hv : LinearIndependent R v
   refine' complete_lattice.independent_def.mp fun i => _
   rw [disjoint_iff_inf_le]
   intro m hm
-  simp only [mem_inf, mem_span_singleton, iSup_subtype', ← span_range_eq_supr] at hm
+  simp only [mem_inf, mem_span_singleton, iSup_subtype', ← span_range_eq_supr] at hm 
   obtain ⟨⟨r, rfl⟩, hm⟩ := hm
   suffices r = 0 by simp [this]
   apply linear_independent_iff_not_smul_mem_span.mp hv i
@@ -964,13 +964,13 @@ theorem exists_maximal_independent (s : ι → M) :
     have h := mt hImaximal _
     swap
     · intro h2
-      rw [h2] at hi
+      rw [h2] at hi 
       exact absurd hiJ hi
     obtain ⟨f, supp_f, sum_f, f_ne⟩ := linear_dependent_comp_subtype.mp h
     have hfi : f i ≠ 0 := by
       contrapose hIlinind
       refine' linear_dependent_comp_subtype.mpr ⟨f, _, sum_f, f_ne⟩
-      simp only [Finsupp.mem_supported, hJ] at supp_f⊢
+      simp only [Finsupp.mem_supported, hJ] at supp_f ⊢
       rintro x hx
       refine' (memJ.mp (supp_f hx)).resolve_left _
       rintro rfl
@@ -978,7 +978,7 @@ theorem exists_maximal_independent (s : ι → M) :
     use f i, hfi
     have hfi' : i ∈ f.support := finsupp.mem_support_iff.mpr hfi
     rw [← Finset.insert_erase hfi', Finset.sum_insert (Finset.not_mem_erase _ _),
-      add_eq_zero_iff_eq_neg] at sum_f
+      add_eq_zero_iff_eq_neg] at sum_f 
     rw [sum_f]
     refine' neg_mem (sum_mem fun c hc => smul_mem _ _ (subset_span ⟨c, _, rfl⟩))
     exact (memJ.mp (supp_f (Finset.erase_subset _ _ hc))).resolve_left (Finset.ne_of_mem_erase hc)
@@ -1001,8 +1001,8 @@ theorem surjective_of_linearIndependent_of_span [Nontrivial R] (hv : LinearIndep
   have h_total_eq : (Finsupp.total ι M R v) l = (Finsupp.total ι M R v) (Finsupp.single i 1) := by
     rw [h_total_l, Finsupp.total_single, one_smul]
   have l_eq : l = _ := LinearMap.ker_eq_bot.1 hv h_total_eq
-  dsimp only [l] at l_eq
-  rw [← Finsupp.embDomain_eq_mapDomain] at l_eq
+  dsimp only [l] at l_eq 
+  rw [← Finsupp.embDomain_eq_mapDomain] at l_eq 
   rcases Finsupp.single_of_embDomain_single (repr ⟨v i, _⟩) f i (1 : R) zero_ne_one.symm l_eq with
     ⟨i', hi'⟩
   use i'
@@ -1033,7 +1033,7 @@ theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
     (hs : LinearIndependent R (fun x => x : s → M)) (hf_inj : Disjoint (span R s) f.ker) :
     LinearIndependent R (fun x => x : f '' s → M') :=
   by
-  rw [← @Subtype.range_coe _ s] at hf_inj
+  rw [← @Subtype.range_coe _ s] at hf_inj 
   refine' (hs.map hf_inj).to_subtype_range' _
   simp [Set.range_comp f]
 #align linear_independent.image_subtype LinearIndependent.image_subtype
@@ -1043,7 +1043,7 @@ theorem LinearIndependent.inl_union_inr {s : Set M} {t : Set M'}
     (ht : LinearIndependent R (fun x => x : t → M')) :
     LinearIndependent R (fun x => x : inl R M M' '' s ∪ inr R M M' '' t → M × M') :=
   by
-  refine' (hs.image_subtype _).union (ht.image_subtype _) _ <;> [simp;simp;skip]
+  refine' (hs.image_subtype _).union (ht.image_subtype _) _ <;> [simp; simp; skip]
   simp only [span_image]
   simp [disjoint_iff, prod_inf_prod]
 #align linear_independent.inl_union_inr LinearIndependent.inl_union_inr
@@ -1137,7 +1137,7 @@ theorem linearIndependent_monoidHom (G : Type _) [Monoid G] (L : Type _) [CommRi
               _ = (∑ i in insert a s, (g i • i : G → L)) 1 :=
                 by
                 rw [Finset.sum_eq_single a]
-                · intro i his hia; rw [Finset.mem_insert] at his
+                · intro i his hia; rw [Finset.mem_insert] at his 
                   rw [h3 i (his.resolve_left hia), zero_smul]
                 · intro haas; exfalso; apply haas; exact Finset.mem_insert_self a s
               _ = 0 := by rw [hg] <;> rfl
@@ -1333,7 +1333,7 @@ theorem linearIndependent_fin2 {f : Fin 2 → V} :
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ⊆ » t) -/
 theorem exists_linearIndependent_extension (hs : LinearIndependent K (coe : s → V)) (hst : s ⊆ t) :
-    ∃ (b : _)(_ : b ⊆ t), s ⊆ b ∧ t ⊆ span K b ∧ LinearIndependent K (coe : b → V) :=
+    ∃ (b : _) (_ : b ⊆ t), s ⊆ b ∧ t ⊆ span K b ∧ LinearIndependent K (coe : b → V) :=
   by
   rcases zorn_subset_nonempty { b | b ⊆ t ∧ LinearIndependent K (coe : b → V) } _ _ ⟨hst, hs⟩ with
     ⟨b, ⟨bt, bi⟩, sb, h⟩
@@ -1352,7 +1352,7 @@ variable (K t)
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ⊆ » t) -/
 theorem exists_linearIndependent :
-    ∃ (b : _)(_ : b ⊆ t), span K b = span K t ∧ LinearIndependent K (coe : b → V) :=
+    ∃ (b : _) (_ : b ⊆ t), span K b = span K t ∧ LinearIndependent K (coe : b → V) :=
   by
   obtain ⟨b, hb₁, -, hb₂, hb₃⟩ :=
     exists_linearIndependent_extension (linearIndependent_empty K V) (Set.empty_subset t)
@@ -1417,7 +1417,7 @@ theorem exists_of_linearIndependent_of_finite_span {t : Finset V}
       have hb₁s : b₁ ∉ s := fun h =>
         by
         have : b₁ ∈ s ∩ ↑(insert b₁ t) := ⟨h, Finset.mem_insert_self _ _⟩
-        rwa [hst] at this
+        rwa [hst] at this 
       have hb₁s' : b₁ ∉ s' := fun h => hb₁s <| hs' h
       have hst : s ∩ ↑t = ∅ :=
         eq_empty_of_subset_empty <|
@@ -1441,7 +1441,7 @@ theorem exists_of_linearIndependent_of_finite_span {t : Finset V}
           have : s ⊆ (span K (insert b₁ ↑(s' ∪ t)) : Submodule K V) := by
             simpa [insert_eq, -singleton_union, -union_singleton] using hss'
           have hb₁ : b₁ ∈ span K (insert b₂ ↑(s' ∪ t)) := mem_span_insert_exchange (this hb₂s) hb₂t
-          rw [span_insert_eq_span hb₁] at hb₃ <;> simpa using hb₃
+          rw [span_insert_eq_span hb₁] at hb₃  <;> simpa using hb₃
         let ⟨u, hust, hsu, Eq⟩ := ih _ (by simp [insert_subset, hb₂s, hs']) hst this
         ⟨u, Subset.trans hust <| union_subset_union (Subset.refl _) (by simp [subset_insert]), hsu,
           by simp [Eq, hb₂t', hb₁t, hb₁s']⟩

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -83,7 +83,7 @@ noncomputable section
 
 open Function Set Submodule
 
-open Classical BigOperators Cardinal
+open scoped Classical BigOperators Cardinal
 
 universe u

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -112,22 +112,10 @@ def LinearIndependent : Prop :=
 
 variable {R} {v}
 
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 theorem linearIndependent_iff : LinearIndependent R v ↔ ∀ l, Finsupp.total ι M R v l = 0 → l = 0 :=
   by simp [LinearIndependent, LinearMap.ker_eq_bot']
 #align linear_independent_iff linearIndependent_iff
 
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 theorem linearIndependent_iff' :
     LinearIndependent R v ↔
       ∀ s : Finset ι, ∀ g : ι → R, (∑ i in s, g i • v i) = 0 → ∀ i ∈ s, g i = 0 :=
@@ -153,12 +141,6 @@ theorem linearIndependent_iff' :
         by_contradiction fun hni => hni <| hf _ _ hl _ <| Finsupp.mem_support_iff.2 hni⟩
 #align linear_independent_iff' linearIndependent_iff'
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
 theorem linearIndependent_iff'' :
     LinearIndependent R v ↔
@@ -172,12 +154,6 @@ theorem linearIndependent_iff'' :
       exact (if_pos hi).symm⟩
 #align linear_independent_iff'' linearIndependent_iff''
 
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 theorem not_linearIndependent_iff :
     ¬LinearIndependent R v ↔
       ∃ s : Finset ι, ∃ g : ι → R, (∑ i in s, g i • v i) = 0 ∧ ∃ i ∈ s, g i ≠ 0 :=
@@ -186,12 +162,6 @@ theorem not_linearIndependent_iff :
   simp only [exists_prop, not_forall]
 #align not_linear_independent_iff not_linearIndependent_iff
 
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 theorem Fintype.linearIndependent_iff [Fintype ι] :
     LinearIndependent R v ↔ ∀ g : ι → R, (∑ i, g i • v i) = 0 → ∀ i, g i = 0 :=
   by
@@ -203,9 +173,6 @@ theorem Fintype.linearIndependent_iff [Fintype ι] :
   rw [hg i hi, zero_smul]
 #align fintype.linear_independent_iff Fintype.linearIndependent_iff
 
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 /-- A finite family of vectors `v i` is linear independent iff the linear map that sends
 `c : ι → R` to `∑ i, c i • v i` has the trivial kernel. -/
 theorem Fintype.linearIndependent_iff' [Fintype ι] :
@@ -214,33 +181,15 @@ theorem Fintype.linearIndependent_iff' [Fintype ι] :
   by simp [Fintype.linearIndependent_iff, LinearMap.ker_eq_bot', funext_iff] <;> skip
 #align fintype.linear_independent_iff' Fintype.linearIndependent_iff'
 
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 theorem Fintype.not_linearIndependent_iff [Fintype ι] :
     ¬LinearIndependent R v ↔ ∃ g : ι → R, (∑ i, g i • v i) = 0 ∧ ∃ i, g i ≠ 0 := by
   simpa using not_iff_not.2 Fintype.linearIndependent_iff
 #align fintype.not_linear_independent_iff Fintype.not_linearIndependent_iff
 
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 theorem linearIndependent_empty_type [IsEmpty ι] : LinearIndependent R v :=
   linearIndependent_iff.mpr fun v hv => Subsingleton.elim v 0
 #align linear_independent_empty_type linearIndependent_empty_type
 
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 theorem LinearIndependent.ne_zero [Nontrivial R] (i : ι) (hv : LinearIndependent R v) : v i ≠ 0 :=
   fun h =>
   zero_ne_one' R <|
@@ -252,12 +201,6 @@ theorem LinearIndependent.ne_zero [Nontrivial R] (i : ι) (hv : LinearIndependen
         · simp [h])
 #align linear_independent.ne_zero LinearIndependent.ne_zero
 
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 /-- A subfamily of a linearly independent family (i.e., a composition with an injective map) is a
 linearly independent family. -/
 theorem LinearIndependent.comp (h : LinearIndependent R v) (f : ι' → ι) (hf : Injective f) :
@@ -272,19 +215,10 @@ theorem LinearIndependent.comp (h : LinearIndependent R v) (f : ι' → ι) (hf
   rw [Finsupp.mapDomain_apply hf]
 #align linear_independent.comp LinearIndependent.comp
 
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 theorem LinearIndependent.coe_range (i : LinearIndependent R v) :
     LinearIndependent R (coe : range v → M) := by simpa using i.comp _ (range_splitting_injective v)
 #align linear_independent.coe_range LinearIndependent.coe_range
 
-/- warning: linear_independent.map -> LinearIndependent.map is a dubious translation:
-<too large>
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 /-- If `v` is a linearly independent family of vectors and the kernel of a linear map `f` is
 disjoint with the submodule spanned by the vectors of `v`, then `f ∘ v` is a linearly independent
 family of vectors. See also `linear_independent.map'` for a special case assuming `ker f = ⊥`. -/
@@ -302,9 +236,6 @@ theorem LinearIndependent.map (hv : LinearIndependent R v) {f : M →ₗ[R] M'}
   exact fun _ => rfl
 #align linear_independent.map LinearIndependent.map
 
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-<too large>
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 /-- An injective linear map sends linearly independent families of vectors to linearly independent
 families of vectors. See also `linear_independent.map` for a more general statement. -/
 theorem LinearIndependent.map' (hv : LinearIndependent R v) (f : M →ₗ[R] M') (hf_inj : f.ker = ⊥) :
@@ -312,9 +243,6 @@ theorem LinearIndependent.map' (hv : LinearIndependent R v) (f : M →ₗ[R] M')
   hv.map <| by simp [hf_inj]
 #align linear_independent.map' LinearIndependent.map'
 
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-<too large>
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 /-- If the image of a family of vectors under a linear map is linearly independent, then so is
 the original family. -/
 theorem LinearIndependent.of_comp (f : M →ₗ[R] M') (hfv : LinearIndependent R (f ∘ v)) :
@@ -325,9 +253,6 @@ theorem LinearIndependent.of_comp (f : M →ₗ[R] M') (hfv : LinearIndependent
     linearIndependent_iff'.1 hfv s g this i his
 #align linear_independent.of_comp LinearIndependent.of_comp
 
-/- warning: linear_map.linear_independent_iff -> LinearMap.linearIndependent_iff is a dubious translation:
-<too large>
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 /-- If `f` is an injective linear map, then the family `f ∘ v` is linearly independent
 if and only if the family `v` is linearly independent. -/
 protected theorem LinearMap.linearIndependent_iff (f : M →ₗ[R] M') (hf_inj : f.ker = ⊥) :
@@ -335,35 +260,17 @@ protected theorem LinearMap.linearIndependent_iff (f : M →ₗ[R] M') (hf_inj :
   ⟨fun h => h.of_comp f, fun h => h.map <| by simp only [hf_inj, disjoint_bot_right]⟩
 #align linear_map.linear_independent_iff LinearMap.linearIndependent_iff
 
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 @[nontriviality]
 theorem linearIndependent_of_subsingleton [Subsingleton R] : LinearIndependent R v :=
   linearIndependent_iff.2 fun l hl => Subsingleton.elim _ _
 #align linear_independent_of_subsingleton linearIndependent_of_subsingleton
 
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 theorem linearIndependent_equiv (e : ι ≃ ι') {f : ι' → M} :
     LinearIndependent R (f ∘ e) ↔ LinearIndependent R f :=
   ⟨fun h => Function.comp.right_id f ▸ e.self_comp_symm ▸ h.comp _ e.symm.Injective, fun h =>
     h.comp _ e.Injective⟩
 #align linear_independent_equiv linearIndependent_equiv
 
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 theorem linearIndependent_equiv' (e : ι ≃ ι') {f : ι' → M} {g : ι → M} (h : f ∘ e = g) :
     LinearIndependent R g ↔ LinearIndependent R f :=
   h ▸ linearIndependent_equiv e
@@ -386,21 +293,12 @@ theorem linearIndependent_image {ι} {s : Set ι} {f : ι → M} (hf : Set.InjOn
 #align linear_independent_image linearIndependent_image
 -/
 
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 theorem linearIndependent_span (hs : LinearIndependent R v) :
     @LinearIndependent ι R (span R (range v)) (fun i : ι => ⟨v i, subset_span (mem_range_self i)⟩) _
       _ _ :=
   LinearIndependent.of_comp (span R (range v)).Subtype hs
 #align linear_independent_span linearIndependent_span
 
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-<too large>
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 /-- See `linear_independent.fin_cons` for a family of elements in a vector space. -/
 theorem LinearIndependent.fin_cons' {m : ℕ} (x : M) (v : Fin m → M) (hli : LinearIndependent R v)
     (x_ortho : ∀ (c : R) (y : Submodule.span R (Set.range v)), c • x + y = (0 : M) → c = 0) :
@@ -417,12 +315,6 @@ theorem LinearIndependent.fin_cons' {m : ℕ} (x : M) (v : Fin m → M) (hli : L
   exact Fin.cases this (hli _ total_eq) j
 #align linear_independent.fin_cons' LinearIndependent.fin_cons'
 
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 /-- A set of linearly independent vectors in a module `M` over a semiring `K` is also linearly
 independent over a subring `R` of `K`.
 The implementation uses minimal assumptions about the relationship between `R`, `K` and `M`.
@@ -459,12 +351,6 @@ theorem linearIndependent_finset_map_embedding_subtype (s : Set M)
 #align linear_independent_finset_map_embedding_subtype linearIndependent_finset_map_embedding_subtype
 -/
 
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 /-- If every finite set of linearly independent vectors has cardinality at most `n`,
 then the same is true for arbitrary sets of linearly independent vectors.
 -/
@@ -485,9 +371,6 @@ section Subtype
 /-! The following lemmas use the subtype defined by a set in `M` as the index set `ι`. -/
 
 
-/- warning: linear_independent_comp_subtype -> linearIndependent_comp_subtype is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_independent_comp_subtype linearIndependent_comp_subtypeₓ'. -/
 theorem linearIndependent_comp_subtype {s : Set ι} :
     LinearIndependent R (v ∘ coe : s → M) ↔
       ∀ l ∈ Finsupp.supported R R s, (Finsupp.total ι M R v) l = 0 → l = 0 :=
@@ -506,18 +389,12 @@ theorem linearIndependent_comp_subtype {s : Set ι} :
       exacts[fun _ => zero_smul _ _, fun _ _ _ => add_smul _ _ _]
 #align linear_independent_comp_subtype linearIndependent_comp_subtype
 
-/- warning: linear_dependent_comp_subtype' -> linearDependent_comp_subtype' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_dependent_comp_subtype' linearDependent_comp_subtype'ₓ'. -/
 theorem linearDependent_comp_subtype' {s : Set ι} :
     ¬LinearIndependent R (v ∘ coe : s → M) ↔
       ∃ f : ι →₀ R, f ∈ Finsupp.supported R R s ∧ Finsupp.total ι M R v f = 0 ∧ f ≠ 0 :=
   by simp [linearIndependent_comp_subtype]
 #align linear_dependent_comp_subtype' linearDependent_comp_subtype'
 
-/- warning: linear_dependent_comp_subtype -> linearDependent_comp_subtype is a dubious translation:
-<too large>
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 /-- A version of `linear_dependent_comp_subtype'` with `finsupp.total` unfolded. -/
 theorem linearDependent_comp_subtype {s : Set ι} :
     ¬LinearIndependent R (v ∘ coe : s → M) ↔
@@ -525,36 +402,24 @@ theorem linearDependent_comp_subtype {s : Set ι} :
   linearDependent_comp_subtype'
 #align linear_dependent_comp_subtype linearDependent_comp_subtype
 
-/- warning: linear_independent_subtype -> linearIndependent_subtype is a dubious translation:
-<too large>
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 theorem linearIndependent_subtype {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
       ∀ l ∈ Finsupp.supported R R s, (Finsupp.total M M R id) l = 0 → l = 0 :=
   by apply @linearIndependent_comp_subtype _ _ _ id
 #align linear_independent_subtype linearIndependent_subtype
 
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 theorem linearIndependent_comp_subtype_disjoint {s : Set ι} :
     LinearIndependent R (v ∘ coe : s → M) ↔
       Disjoint (Finsupp.supported R R s) (Finsupp.total ι M R v).ker :=
   by rw [linearIndependent_comp_subtype, LinearMap.disjoint_ker]
 #align linear_independent_comp_subtype_disjoint linearIndependent_comp_subtype_disjoint
 
-/- warning: linear_independent_subtype_disjoint -> linearIndependent_subtype_disjoint is a dubious translation:
-<too large>
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 theorem linearIndependent_subtype_disjoint {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
       Disjoint (Finsupp.supported R R s) (Finsupp.total M M R id).ker :=
   by apply @linearIndependent_comp_subtype_disjoint _ _ _ id
 #align linear_independent_subtype_disjoint linearIndependent_subtype_disjoint
 
-/- warning: linear_independent_iff_total_on -> linearIndependent_iff_totalOn is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_independent_iff_total_on linearIndependent_iff_totalOnₓ'. -/
 theorem linearIndependent_iff_totalOn {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔ (Finsupp.totalOn M M R id s).ker = ⊥ := by
   rw [Finsupp.totalOn, LinearMap.ker, LinearMap.comap_codRestrict, Submodule.map_bot, comap_bot,
@@ -562,12 +427,6 @@ theorem linearIndependent_iff_totalOn {s : Set M} :
     map_comap_subtype, map_le_iff_le_comap, comap_bot, ker_subtype, le_bot_iff]
 #align linear_independent_iff_total_on linearIndependent_iff_totalOn
 
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 theorem LinearIndependent.restrict_of_comp_subtype {s : Set ι}
     (hs : LinearIndependent R (v ∘ coe : s → M)) : LinearIndependent R (s.restrict v) :=
   hs
@@ -654,33 +513,15 @@ variable [Module R M] [Module R M'] [Module R M'']
 
 variable {a b : R} {x y : M}
 
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 theorem linearIndependent_iff_injective_total :
     LinearIndependent R v ↔ Function.Injective (Finsupp.total ι M R v) :=
   linearIndependent_iff.trans
     (injective_iff_map_eq_zero (Finsupp.total ι M R v).toAddMonoidHom).symm
 #align linear_independent_iff_injective_total linearIndependent_iff_injective_total
 
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 alias linearIndependent_iff_injective_total ↔ LinearIndependent.injective_total _
 #align linear_independent.injective_total LinearIndependent.injective_total
 
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 theorem LinearIndependent.injective [Nontrivial R] (hv : LinearIndependent R v) : Injective v :=
   by
   intro i j hij
@@ -696,12 +537,6 @@ theorem LinearIndependent.injective [Nontrivial R] (hv : LinearIndependent R v)
   simpa [Finsupp.single_eq_single_iff] using h_single_eq
 #align linear_independent.injective LinearIndependent.injective
 
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 theorem LinearIndependent.to_subtype_range {ι} {f : ι → M} (hf : LinearIndependent R f) :
     LinearIndependent R (coe : range f → M) :=
   by
@@ -709,23 +544,11 @@ theorem LinearIndependent.to_subtype_range {ι} {f : ι → M} (hf : LinearIndep
   exact (linearIndependent_subtype_range hf.injective).2 hf
 #align linear_independent.to_subtype_range LinearIndependent.to_subtype_range
 
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 theorem LinearIndependent.to_subtype_range' {ι} {f : ι → M} (hf : LinearIndependent R f) {t}
     (ht : range f = t) : LinearIndependent R (coe : t → M) :=
   ht ▸ hf.to_subtype_range
 #align linear_independent.to_subtype_range' LinearIndependent.to_subtype_range'
 
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 theorem LinearIndependent.image_of_comp {ι ι'} (s : Set ι) (f : ι → ι') (g : ι' → M)
     (hs : LinearIndependent R fun x : s => g (f x)) : LinearIndependent R fun x : f '' s => g x :=
   by
@@ -734,20 +557,11 @@ theorem LinearIndependent.image_of_comp {ι ι'} (s : Set ι) (f : ι → ι') (
   exact (linearIndependent_equiv' (Equiv.Set.imageOfInjOn f s this) rfl).1 hs
 #align linear_independent.image_of_comp LinearIndependent.image_of_comp
 
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 theorem LinearIndependent.image {ι} {s : Set ι} {f : ι → M}
     (hs : LinearIndependent R fun x : s => f x) : LinearIndependent R fun x : f '' s => (x : M) :=
   by convert LinearIndependent.image_of_comp s f id hs
 #align linear_independent.image LinearIndependent.image
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_independent.group_smul LinearIndependent.group_smulₓ'. -/
 theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulAction G R]
     [DistribMulAction G M] [IsScalarTower G R M] [SMulCommClass G R M] {v : ι → M}
     (hv : LinearIndependent R v) (w : ι → G) : LinearIndependent R (w • v) :=
@@ -762,12 +576,6 @@ theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulActi
     intros ; erw [Pi.smul_apply, smul_assoc, smul_comm]
 #align linear_independent.group_smul LinearIndependent.group_smul
 
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-Case conversion may be inaccurate. Consider using '#align linear_independent.units_smul LinearIndependent.units_smulₓ'. -/
 -- This lemma cannot be proved with `linear_independent.group_smul` since the action of
 -- `Rˣ` on `R` is not commutative.
 theorem LinearIndependent.units_smul {v : ι → M} (hv : LinearIndependent R v) (w : ι → Rˣ) :
@@ -826,12 +634,6 @@ theorem LinearIndependent.maximal_iff {ι : Type w} {R : Type u} [Ring R] [Nontr
 
 end Maximal
 
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-Case conversion may be inaccurate. Consider using '#align linear_independent.eq_of_smul_apply_eq_smul_apply LinearIndependent.eq_of_smul_apply_eq_smul_applyₓ'. -/
 /-- Linear independent families are injective, even if you multiply either side. -/
 theorem LinearIndependent.eq_of_smul_apply_eq_smul_apply {M : Type _} [AddCommGroup M] [Module R M]
     {v : ι → M} (li : LinearIndependent R v) (c d : R) (i j : ι) (hc : c ≠ 0)
@@ -856,12 +658,6 @@ section Subtype
 /-! The following lemmas use the subtype defined by a set in `M` as the index set `ι`. -/
 
 
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-Case conversion may be inaccurate. Consider using '#align linear_independent.disjoint_span_image LinearIndependent.disjoint_span_imageₓ'. -/
 theorem LinearIndependent.disjoint_span_image (hv : LinearIndependent R v) {s t : Set ι}
     (hs : Disjoint s t) : Disjoint (Submodule.span R <| v '' s) (Submodule.span R <| v '' t) :=
   by
@@ -872,12 +668,6 @@ theorem LinearIndependent.disjoint_span_image (hv : LinearIndependent R v) {s t
   simp [this]
 #align linear_independent.disjoint_span_image LinearIndependent.disjoint_span_image
 
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 theorem LinearIndependent.not_mem_span_image [Nontrivial R] (hv : LinearIndependent R v) {s : Set ι}
     {x : ι} (h : x ∉ s) : v x ∉ Submodule.span R (v '' s) :=
   by
@@ -891,9 +681,6 @@ theorem LinearIndependent.not_mem_span_image [Nontrivial R] (hv : LinearIndepend
   simpa using h
 #align linear_independent.not_mem_span_image LinearIndependent.not_mem_span_image
 
-/- warning: linear_independent.total_ne_of_not_mem_support -> LinearIndependent.total_ne_of_not_mem_support is a dubious translation:
-<too large>
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 theorem LinearIndependent.total_ne_of_not_mem_support [Nontrivial R] (hv : LinearIndependent R v)
     {x : ι} (f : ι →₀ R) (h : x ∉ f.support) : Finsupp.total ι M R v f ≠ v x :=
   by
@@ -906,12 +693,6 @@ theorem LinearIndependent.total_ne_of_not_mem_support [Nontrivial R] (hv : Linea
   exact p f (f.mem_supported_support R) rfl
 #align linear_independent.total_ne_of_not_mem_support LinearIndependent.total_ne_of_not_mem_support
 
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 theorem linearIndependent_sum {v : Sum ι ι' → M} :
     LinearIndependent R v ↔
       LinearIndependent R (v ∘ Sum.inl) ∧
@@ -947,12 +728,6 @@ theorem linearIndependent_sum {v : Sum ι ι' → M} :
     · exact smul_mem _ _ (subset_span ⟨Sum.inr i, mem_range_self _, rfl⟩)
 #align linear_independent_sum linearIndependent_sum
 
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 theorem LinearIndependent.sum_type {v' : ι' → M} (hv : LinearIndependent R v)
     (hv' : LinearIndependent R v')
     (h : Disjoint (Submodule.span R (range v)) (Submodule.span R (range v'))) :
@@ -960,24 +735,12 @@ theorem LinearIndependent.sum_type {v' : ι' → M} (hv : LinearIndependent R v)
   linearIndependent_sum.2 ⟨hv, hv', h⟩
 #align linear_independent.sum_type LinearIndependent.sum_type
 
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 theorem LinearIndependent.union {s t : Set M} (hs : LinearIndependent R (fun x => x : s → M))
     (ht : LinearIndependent R (fun x => x : t → M)) (hst : Disjoint (span R s) (span R t)) :
     LinearIndependent R (fun x => x : s ∪ t → M) :=
   (hs.sum_type ht <| by simpa).to_subtype_range' <| by simp
 #align linear_independent.union LinearIndependent.union
 
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 theorem linearIndependent_iUnion_finite_subtype {ι : Type _} {f : ι → Set M}
     (hl : ∀ i, LinearIndependent R (fun x => x : f i → M))
     (hd : ∀ i, ∀ t : Set ι, t.Finite → i ∉ t → Disjoint (span R (f i)) (⨆ i ∈ t, span R (f i))) :
@@ -997,12 +760,6 @@ theorem linearIndependent_iUnion_finite_subtype {ι : Type _} {f : ι → Set M}
     exact hd i s s.finite_to_set his
 #align linear_independent_Union_finite_subtype linearIndependent_iUnion_finite_subtype
 
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-Case conversion may be inaccurate. Consider using '#align linear_independent_Union_finite linearIndependent_iUnion_finiteₓ'. -/
 theorem linearIndependent_iUnion_finite {η : Type _} {ιs : η → Type _} {f : ∀ j : η, ιs j → M}
     (hindep : ∀ j, LinearIndependent R (f j))
     (hd :
@@ -1039,12 +796,6 @@ section repr
 
 variable (hv : LinearIndependent R v)
 
-/- warning: linear_independent.total_equiv -> LinearIndependent.totalEquiv is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align linear_independent.total_equiv LinearIndependent.totalEquivₓ'. -/
 /-- Canonical isomorphism between linear combinations and the span of linearly independent vectors.
 -/
 @[simps (config := { rhsMd := semireducible })]
@@ -1064,12 +815,6 @@ def LinearIndependent.totalEquiv (hv : LinearIndependent R v) : (ι →₀ R) 
     apply mem_range_self l
 #align linear_independent.total_equiv LinearIndependent.totalEquiv
 
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-Case conversion may be inaccurate. Consider using '#align linear_independent.repr LinearIndependent.reprₓ'. -/
 /-- Linear combination representing a vector in the span of linearly independent vectors.
 
 Given a family of linearly independent vectors, we can represent any vector in their span as
@@ -1079,39 +824,24 @@ def LinearIndependent.repr (hv : LinearIndependent R v) : span R (range v) →
   hv.totalEquiv.symm
 #align linear_independent.repr LinearIndependent.repr
 
-/- warning: linear_independent.total_repr -> LinearIndependent.total_repr is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_independent.total_repr LinearIndependent.total_reprₓ'. -/
 @[simp]
 theorem LinearIndependent.total_repr (x) : Finsupp.total ι M R v (hv.repr x) = x :=
   Subtype.ext_iff.1 (LinearEquiv.apply_symm_apply hv.totalEquiv x)
 #align linear_independent.total_repr LinearIndependent.total_repr
 
-/- warning: linear_independent.total_comp_repr -> LinearIndependent.total_comp_repr is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_independent.total_comp_repr LinearIndependent.total_comp_reprₓ'. -/
 theorem LinearIndependent.total_comp_repr :
     (Finsupp.total ι M R v).comp hv.repr = Submodule.subtype _ :=
   LinearMap.ext <| hv.total_repr
 #align linear_independent.total_comp_repr LinearIndependent.total_comp_repr
 
-/- warning: linear_independent.repr_ker -> LinearIndependent.repr_ker is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_independent.repr_ker LinearIndependent.repr_kerₓ'. -/
 theorem LinearIndependent.repr_ker : hv.repr.ker = ⊥ := by
   rw [LinearIndependent.repr, LinearEquiv.ker]
 #align linear_independent.repr_ker LinearIndependent.repr_ker
 
-/- warning: linear_independent.repr_range -> LinearIndependent.repr_range is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_independent.repr_range LinearIndependent.repr_rangeₓ'. -/
 theorem LinearIndependent.repr_range : hv.repr.range = ⊤ := by
   rw [LinearIndependent.repr, LinearEquiv.range]
 #align linear_independent.repr_range LinearIndependent.repr_range
 
-/- warning: linear_independent.repr_eq -> LinearIndependent.repr_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq LinearIndependent.repr_eqₓ'. -/
 theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M R v l = ↑x) :
     hv.repr x = l :=
   by
@@ -1128,18 +858,12 @@ theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M
   rfl
 #align linear_independent.repr_eq LinearIndependent.repr_eq
 
-/- warning: linear_independent.repr_eq_single -> LinearIndependent.repr_eq_single is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq_single LinearIndependent.repr_eq_singleₓ'. -/
 theorem LinearIndependent.repr_eq_single (i) (x) (hx : ↑x = v i) : hv.repr x = Finsupp.single i 1 :=
   by
   apply hv.repr_eq
   simp [Finsupp.total_single, hx]
 #align linear_independent.repr_eq_single LinearIndependent.repr_eq_single
 
-/- warning: linear_independent.span_repr_eq -> LinearIndependent.span_repr_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_independent.span_repr_eq LinearIndependent.span_repr_eqₓ'. -/
 theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
     Span.repr R (Set.range v) x = (hv.repr x).equivMapDomain (Equiv.ofInjective _ hv.Injective) :=
   by
@@ -1155,12 +879,6 @@ theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
   simp [← p]
 #align linear_independent.span_repr_eq LinearIndependent.span_repr_eq
 
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-Case conversion may be inaccurate. Consider using '#align linear_independent_iff_not_smul_mem_span linearIndependent_iff_not_smul_mem_spanₓ'. -/
 -- TODO: why is this so slow?
 theorem linearIndependent_iff_not_smul_mem_span :
     LinearIndependent R v ↔ ∀ (i : ι) (a : R), a • v i ∈ span R (v '' (univ \ {i})) → a = 0 :=
@@ -1184,12 +902,6 @@ theorem linearIndependent_iff_not_smul_mem_span :
       · simp [hl]⟩
 #align linear_independent_iff_not_smul_mem_span linearIndependent_iff_not_smul_mem_span
 
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-Case conversion may be inaccurate. Consider using '#align linear_independent.independent_span_singleton LinearIndependent.independent_span_singletonₓ'. -/
 /-- See also `complete_lattice.independent_iff_linear_independent_of_ne_zero`. -/
 theorem LinearIndependent.independent_span_singleton (hv : LinearIndependent R v) :
     CompleteLattice.Independent fun i => R ∙ v i :=
@@ -1208,9 +920,6 @@ theorem LinearIndependent.independent_span_singleton (hv : LinearIndependent R v
 
 variable (R)
 
-/- warning: exists_maximal_independent' -> exists_maximal_independent' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align exists_maximal_independent' exists_maximal_independent'ₓ'. -/
 theorem exists_maximal_independent' (s : ι → M) :
     ∃ I : Set ι,
       (LinearIndependent R fun x : I => s x) ∧
@@ -1238,9 +947,6 @@ theorem exists_maximal_independent' (s : ι → M) :
   exact ⟨I, hli, fun J hsub hli => Set.Subset.antisymm hsub (hmax ⟨J, hli⟩ hsub)⟩
 #align exists_maximal_independent' exists_maximal_independent'
 
-/- warning: exists_maximal_independent -> exists_maximal_independent is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align exists_maximal_independent exists_maximal_independentₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » I) -/
 theorem exists_maximal_independent (s : ι → M) :
     ∃ I : Set ι,
@@ -1280,12 +986,6 @@ theorem exists_maximal_independent (s : ι → M) :
 
 end repr
 
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 theorem surjective_of_linearIndependent_of_span [Nontrivial R] (hv : LinearIndependent R v)
     (f : ι' ↪ ι) (hss : range v ⊆ span R (range (v ∘ f))) : Surjective f :=
   by
@@ -1309,12 +1009,6 @@ theorem surjective_of_linearIndependent_of_span [Nontrivial R] (hv : LinearIndep
   exact hi'.2
 #align surjective_of_linear_independent_of_span surjective_of_linearIndependent_of_span
 
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 theorem eq_of_linearIndependent_of_span_subtype [Nontrivial R] {s t : Set M}
     (hs : LinearIndependent R (fun x => x : s → M)) (h : t ⊆ s) (hst : s ⊆ span R t) : s = t :=
   by
@@ -1335,9 +1029,6 @@ theorem eq_of_linearIndependent_of_span_subtype [Nontrivial R] {s t : Set M}
 
 open LinearMap
 
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 theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
     (hs : LinearIndependent R (fun x => x : s → M)) (hf_inj : Disjoint (span R s) f.ker) :
     LinearIndependent R (fun x => x : f '' s → M') :=
@@ -1347,9 +1038,6 @@ theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
   simp [Set.range_comp f]
 #align linear_independent.image_subtype LinearIndependent.image_subtype
 
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 theorem LinearIndependent.inl_union_inr {s : Set M} {t : Set M'}
     (hs : LinearIndependent R (fun x => x : s → M))
     (ht : LinearIndependent R (fun x => x : t → M')) :
@@ -1360,9 +1048,6 @@ theorem LinearIndependent.inl_union_inr {s : Set M} {t : Set M'}
   simp [disjoint_iff, prod_inf_prod]
 #align linear_independent.inl_union_inr LinearIndependent.inl_union_inr
 
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 theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv : LinearIndependent R v)
     (hv' : LinearIndependent R v') :
     LinearIndependent R (Sum.elim (inl R M M' ∘ v) (inr R M M' ∘ v')) :=
@@ -1371,12 +1056,6 @@ theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv :
       simp only [span_le, range_coe, range_comp_subset_range]
 #align linear_independent_inl_union_inr' linearIndependent_inl_union_inr'
 
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 -- See, for example, Keith Conrad's note
 --  <https://kconrad.math.uconn.edu/blurbs/galoistheory/linearchar.pdf>
 /-- Dedekind's linear independence of characters -/
@@ -1470,12 +1149,6 @@ theorem linearIndependent_monoidHom (G : Type _) [Monoid G] (L : Type _) [CommRi
             ⟨h4, h3⟩
 #align linear_independent_monoid_hom linearIndependent_monoidHom
 
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 theorem le_of_span_le_span [Nontrivial R] {s t u : Set M} (hl : LinearIndependent R (coe : u → M))
     (hsu : s ⊆ u) (htu : t ⊆ u) (hst : span R s ≤ span R t) : s ⊆ t :=
   by
@@ -1485,12 +1158,6 @@ theorem le_of_span_le_span [Nontrivial R] {s t u : Set M} (hl : LinearIndependen
   rw [← this]; apply Set.subset_union_left
 #align le_of_span_le_span le_of_span_le_span
 
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-Case conversion may be inaccurate. Consider using '#align span_le_span_iff span_le_span_iffₓ'. -/
 theorem span_le_span_iff [Nontrivial R] {s t u : Set M} (hl : LinearIndependent R (coe : u → M))
     (hsu : s ⊆ u) (htu : t ⊆ u) : span R s ≤ span R t ↔ s ⊆ t :=
   ⟨le_of_span_le_span hl hsu htu, span_mono⟩
@@ -1506,12 +1173,6 @@ variable [Module R M] [NoZeroSMulDivisors R M] [Module R M']
 
 variable {v : ι → M} {s t : Set M} {x y z : M}
 
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-Case conversion may be inaccurate. Consider using '#align linear_independent_unique_iff linearIndependent_unique_iffₓ'. -/
 theorem linearIndependent_unique_iff (v : ι → M) [Unique ι] :
     LinearIndependent R v ↔ v default ≠ 0 :=
   by
@@ -1521,21 +1182,9 @@ theorem linearIndependent_unique_iff (v : ι → M) [Unique ι] :
   exact one_ne_zero (Finsupp.single_eq_zero.1 this)
 #align linear_independent_unique_iff linearIndependent_unique_iff
 
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 alias linearIndependent_unique_iff ↔ _ linearIndependent_unique
 #align linear_independent_unique linearIndependent_unique
 
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 theorem linearIndependent_singleton {x : M} (hx : x ≠ 0) :
     LinearIndependent R (fun x => x : ({x} : Set M) → M) :=
   linearIndependent_unique coe hx
@@ -1560,12 +1209,6 @@ variable {v : ι → V} {s t : Set V} {x y z : V}
 
 open Submodule
 
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 /- TODO: some of the following proofs can generalized with a zero_ne_one predicate type class
    (instead of a data containing type class) -/
 theorem mem_span_insert_exchange :
@@ -1578,12 +1221,6 @@ theorem mem_span_insert_exchange :
   simp [a0, smul_add, smul_smul]
 #align mem_span_insert_exchange mem_span_insert_exchange
 
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 theorem linearIndependent_iff_not_mem_span :
     LinearIndependent K v ↔ ∀ i, v i ∉ span K (v '' (univ \ {i})) :=
   by
@@ -1596,12 +1233,6 @@ theorem linearIndependent_iff_not_mem_span :
     exact False.elim (h _ ((smul_mem_iff _ ha').1 ha))
 #align linear_independent_iff_not_mem_span linearIndependent_iff_not_mem_span
 
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 theorem LinearIndependent.insert (hs : LinearIndependent K (fun b => b : s → V))
     (hx : x ∉ span K s) : LinearIndependent K (fun b => b : insert x s → V) :=
   by
@@ -1611,12 +1242,6 @@ theorem LinearIndependent.insert (hs : LinearIndependent K (fun b => b : s → V
   rwa [disjoint_span_singleton' x0]
 #align linear_independent.insert LinearIndependent.insert
 
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 theorem linearIndependent_option' :
     LinearIndependent K (fun o => Option.casesOn' o x v : Option ι → V) ↔
       LinearIndependent K v ∧ x ∉ Submodule.span K (range v) :=
@@ -1629,33 +1254,18 @@ theorem linearIndependent_option' :
   exact h.2 (zero_mem _)
 #align linear_independent_option' linearIndependent_option'
 
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 theorem LinearIndependent.option (hv : LinearIndependent K v)
     (hx : x ∉ Submodule.span K (range v)) :
     LinearIndependent K (fun o => Option.casesOn' o x v : Option ι → V) :=
   linearIndependent_option'.2 ⟨hv, hx⟩
 #align linear_independent.option LinearIndependent.option
 
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 theorem linearIndependent_option {v : Option ι → V} :
     LinearIndependent K v ↔
       LinearIndependent K (v ∘ coe : ι → V) ∧ v none ∉ Submodule.span K (range (v ∘ coe : ι → V)) :=
   by simp only [← linearIndependent_option', Option.casesOn'_none_coe]
 #align linear_independent_option linearIndependent_option
 
-/- warning: linear_independent_insert' -> linearIndependent_insert' is a dubious translation:
-<too large>
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 theorem linearIndependent_insert' {ι} {s : Set ι} {a : ι} {f : ι → V} (has : a ∉ s) :
     (LinearIndependent K fun x : insert a s => f x) ↔
       (LinearIndependent K fun x : s => f x) ∧ f a ∉ Submodule.span K (f '' s) :=
@@ -1665,36 +1275,18 @@ theorem linearIndependent_insert' {ι} {s : Set ι} {a : ι} {f : ι → V} (has
   simp [(· ∘ ·), range_comp f]
 #align linear_independent_insert' linearIndependent_insert'
 
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 theorem linearIndependent_insert (hxs : x ∉ s) :
     (LinearIndependent K fun b : insert x s => (b : V)) ↔
       (LinearIndependent K fun b : s => (b : V)) ∧ x ∉ Submodule.span K s :=
   (@linearIndependent_insert' _ _ _ _ _ _ _ _ id hxs).trans <| by simp
 #align linear_independent_insert linearIndependent_insert
 
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 theorem linearIndependent_pair {x y : V} (hx : x ≠ 0) (hy : ∀ a : K, a • x ≠ y) :
     LinearIndependent K (coe : ({x, y} : Set V) → V) :=
   pair_comm y x ▸ (linearIndependent_singleton hx).insert <|
     mt mem_span_singleton.1 (not_exists.2 hy)
 #align linear_independent_pair linearIndependent_pair
 
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-Case conversion may be inaccurate. Consider using '#align linear_independent_fin_cons linearIndependent_fin_consₓ'. -/
 theorem linearIndependent_fin_cons {n} {v : Fin n → V} :
     LinearIndependent K (Fin.cons x v : Fin (n + 1) → V) ↔
       LinearIndependent K v ∧ x ∉ Submodule.span K (range v) :=
@@ -1708,24 +1300,12 @@ theorem linearIndependent_fin_cons {n} {v : Fin n → V} :
     rw [comp_app, comp_app, finSuccEquiv_symm_some, Fin.cons_succ]
 #align linear_independent_fin_cons linearIndependent_fin_cons
 
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-Case conversion may be inaccurate. Consider using '#align linear_independent_fin_snoc linearIndependent_fin_snocₓ'. -/
 theorem linearIndependent_fin_snoc {n} {v : Fin n → V} :
     LinearIndependent K (Fin.snoc v x : Fin (n + 1) → V) ↔
       LinearIndependent K v ∧ x ∉ Submodule.span K (range v) :=
   by rw [Fin.snoc_eq_cons_rotate, linearIndependent_equiv, linearIndependent_fin_cons]
 #align linear_independent_fin_snoc linearIndependent_fin_snoc
 
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-Case conversion may be inaccurate. Consider using '#align linear_independent.fin_cons LinearIndependent.fin_consₓ'. -/
 /-- See `linear_independent.fin_cons'` for an uglier version that works if you
 only have a module over a semiring. -/
 theorem LinearIndependent.fin_cons {n} {v : Fin n → V} (hv : LinearIndependent K v)
@@ -1733,48 +1313,24 @@ theorem LinearIndependent.fin_cons {n} {v : Fin n → V} (hv : LinearIndependent
   linearIndependent_fin_cons.2 ⟨hv, hx⟩
 #align linear_independent.fin_cons LinearIndependent.fin_cons
 
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-Case conversion may be inaccurate. Consider using '#align linear_independent_fin_succ linearIndependent_fin_succₓ'. -/
 theorem linearIndependent_fin_succ {n} {v : Fin (n + 1) → V} :
     LinearIndependent K v ↔
       LinearIndependent K (Fin.tail v) ∧ v 0 ∉ Submodule.span K (range <| Fin.tail v) :=
   by rw [← linearIndependent_fin_cons, Fin.cons_self_tail]
 #align linear_independent_fin_succ linearIndependent_fin_succ
 
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 theorem linearIndependent_fin_succ' {n} {v : Fin (n + 1) → V} :
     LinearIndependent K v ↔
       LinearIndependent K (Fin.init v) ∧ v (Fin.last _) ∉ Submodule.span K (range <| Fin.init v) :=
   by rw [← linearIndependent_fin_snoc, Fin.snoc_init_self]
 #align linear_independent_fin_succ' linearIndependent_fin_succ'
 
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 theorem linearIndependent_fin2 {f : Fin 2 → V} :
     LinearIndependent K f ↔ f 1 ≠ 0 ∧ ∀ a : K, a • f 1 ≠ f 0 := by
   rw [linearIndependent_fin_succ, linearIndependent_unique_iff, range_unique, mem_span_singleton,
     not_exists, show Fin.tail f default = f 1 by rw [← Fin.succ_zero_eq_one] <;> rfl]
 #align linear_independent_fin2 linearIndependent_fin2
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ⊆ » t) -/
 theorem exists_linearIndependent_extension (hs : LinearIndependent K (coe : s → V)) (hst : s ⊆ t) :
     ∃ (b : _)(_ : b ⊆ t), s ⊆ b ∧ t ⊆ span K b ∧ LinearIndependent K (coe : b → V) :=
@@ -1794,12 +1350,6 @@ theorem exists_linearIndependent_extension (hs : LinearIndependent K (coe : s 
 
 variable (K t)
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ⊆ » t) -/
 theorem exists_linearIndependent :
     ∃ (b : _)(_ : b ⊆ t), span K b = span K t ∧ LinearIndependent K (coe : b → V) :=
@@ -1820,48 +1370,24 @@ noncomputable def LinearIndependent.extend (hs : LinearIndependent K (fun x => x
 #align linear_independent.extend LinearIndependent.extend
 -/
 
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 theorem LinearIndependent.extend_subset (hs : LinearIndependent K (fun x => x : s → V))
     (hst : s ⊆ t) : hs.extend hst ⊆ t :=
   let ⟨hbt, hsb, htb, hli⟩ := Classical.choose_spec (exists_linearIndependent_extension hs hst)
   hbt
 #align linear_independent.extend_subset LinearIndependent.extend_subset
 
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 theorem LinearIndependent.subset_extend (hs : LinearIndependent K (fun x => x : s → V))
     (hst : s ⊆ t) : s ⊆ hs.extend hst :=
   let ⟨hbt, hsb, htb, hli⟩ := Classical.choose_spec (exists_linearIndependent_extension hs hst)
   hsb
 #align linear_independent.subset_extend LinearIndependent.subset_extend
 
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 theorem LinearIndependent.subset_span_extend (hs : LinearIndependent K (fun x => x : s → V))
     (hst : s ⊆ t) : t ⊆ span K (hs.extend hst) :=
   let ⟨hbt, hsb, htb, hli⟩ := Classical.choose_spec (exists_linearIndependent_extension hs hst)
   htb
 #align linear_independent.subset_span_extend LinearIndependent.subset_span_extend
 
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 theorem LinearIndependent.linearIndependent_extend (hs : LinearIndependent K (fun x => x : s → V))
     (hst : s ⊆ t) : LinearIndependent K (coe : hs.extend hst → V) :=
   let ⟨hbt, hsb, htb, hli⟩ := Classical.choose_spec (exists_linearIndependent_extension hs hst)
@@ -1870,12 +1396,6 @@ theorem LinearIndependent.linearIndependent_extend (hs : LinearIndependent K (fu
 
 variable {K V}
 
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 -- TODO(Mario): rewrite?
 theorem exists_of_linearIndependent_of_finite_span {t : Finset V}
     (hs : LinearIndependent K (fun x => x : s → V)) (hst : s ⊆ (span K ↑t : Submodule K V)) :
@@ -1939,12 +1459,6 @@ theorem exists_of_linearIndependent_of_finite_span {t : Finset V}
       h.2.1, by simp only [h.2.2, Eq]⟩
 #align exists_of_linear_independent_of_finite_span exists_of_linearIndependent_of_finite_span
 
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 theorem exists_finite_card_le_of_finite_of_linearIndependent_of_span (ht : t.Finite)
     (hs : LinearIndependent K (fun x => x : s → V)) (hst : s ⊆ span K t) :
     ∃ h : s.Finite, h.toFinset.card ≤ ht.toFinset.card :=

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -501,8 +501,7 @@ theorem linearIndependent_comp_subtype {s : Set ι} :
   · intro h l hl
     refine' Finsupp.embDomain_eq_zero.1 (h (l.emb_domain <| Function.Embedding.subtype s) _ _)
     · suffices ∀ i hi, ¬l ⟨i, hi⟩ = 0 → i ∈ s by simpa
-      intros
-      assumption
+      intros ; assumption
     · rwa [Finsupp.embDomain_eq_mapDomain, Finsupp.sum_mapDomain_index]
       exacts[fun _ => zero_smul _ _, fun _ _ _ => add_smul _ _ _]
 #align linear_independent_comp_subtype linearIndependent_comp_subtype
@@ -615,8 +614,7 @@ theorem linearIndependent_iUnion_of_directed {η : Type _} {s : η → Set M} (h
     rcases hs.finset_le fi.to_finset with ⟨i, hi⟩
     exact (h i).mono (subset.trans hI <| Union₂_subset fun j hj => hi j (fi.mem_to_finset.2 hj))
   · refine' (linearIndependent_empty _ _).mono _
-    rintro _ ⟨_, ⟨i, _⟩, _⟩
-    exact hη ⟨i⟩
+    rintro _ ⟨_, ⟨i, _⟩, _⟩; exact hη ⟨i⟩
 #align linear_independent_Union_of_directed linearIndependent_iUnion_of_directed
 -/
 
@@ -761,8 +759,7 @@ theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulActi
   · dsimp only
     exact (hgs i hi).symm ▸ smul_zero _
   · rw [← hsum, Finset.sum_congr rfl _]
-    intros
-    erw [Pi.smul_apply, smul_assoc, smul_comm]
+    intros ; erw [Pi.smul_apply, smul_assoc, smul_comm]
 #align linear_independent.group_smul LinearIndependent.group_smul
 
 /- warning: linear_independent.units_smul -> LinearIndependent.units_smul is a dubious translation:
@@ -819,11 +816,7 @@ theorem LinearIndependent.maximal_iff {ι : Type w} {R : Type u} [Ring R] [Nontr
     rw [range_comp, ← @image_univ _ _ w] at p
     exact range_iff_surjective.mp (image_injective.mpr i'.injective p)
   · intro p w i' h
-    specialize
-      p w (coe : w → M) i' (fun i => ⟨v i, range_subset_iff.mp h i⟩)
-        (by
-          ext
-          simp)
+    specialize p w (coe : w → M) i' (fun i => ⟨v i, range_subset_iff.mp h i⟩) (by ext; simp)
     have q := congr_arg (fun s => (coe : w → M) '' s) p.range_eq
     dsimp at q
     rw [← image_univ, image_image] at q
@@ -1465,13 +1458,9 @@ theorem linearIndependent_monoidHom (G : Type _) [Monoid G] (L : Type _) [CommRi
               _ = (∑ i in insert a s, (g i • i : G → L)) 1 :=
                 by
                 rw [Finset.sum_eq_single a]
-                · intro i his hia
-                  rw [Finset.mem_insert] at his
+                · intro i his hia; rw [Finset.mem_insert] at his
                   rw [h3 i (his.resolve_left hia), zero_smul]
-                · intro haas
-                  exfalso
-                  apply haas
-                  exact Finset.mem_insert_self a s
+                · intro haas; exfalso; apply haas; exact Finset.mem_insert_self a s
               _ = 0 := by rw [hg] <;> rfl
               
           (-- Now we're done; the last two facts together imply that `g` vanishes on every element
@@ -1585,9 +1574,7 @@ theorem mem_span_insert_exchange :
   simp [mem_span_insert]
   rintro a z hz rfl h
   refine' ⟨a⁻¹, -a⁻¹ • z, smul_mem _ _ hz, _⟩
-  have a0 : a ≠ 0 := by
-    rintro rfl
-    simp_all
+  have a0 : a ≠ 0 := by rintro rfl; simp_all
   simp [a0, smul_add, smul_smul]
 #align mem_span_insert_exchange mem_span_insert_exchange

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -204,10 +204,7 @@ theorem Fintype.linearIndependent_iff [Fintype ι] :
 #align fintype.linear_independent_iff Fintype.linearIndependent_iff
 
 /- warning: fintype.linear_independent_iff' -> Fintype.linearIndependent_iff' is a dubious translation:
-lean 3 declaration is
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_inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.module.{u2, u2, 0, u2, u3} R R Nat ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.module.{u2, u2, 0, max u1 u2, u3} R R Nat (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) => (forall (i : ι), LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) -> (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (forall (i : ι), (fun (i : ι) => R) i) M (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5)) (LinearEquiv.hasCoeToFun.{0, 0, max u1 u2 u3, max (max u1 u2) u3} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (forall (i : ι), (fun (i : ι) => R) i) M (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, max u2 u3} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u1 u2, u3} R R (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) 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Semiring.toModule.{u2} R _inst_1) i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.module.{u2, u2, 0, u2, u3} R R Nat ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R 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ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) Nat _inst_2 _inst_5 _inst_8 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u1} ι a b)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5))) (fun (i : ι) => LinearMap.smulRight.{u2, u2, u3, u2} R ((fun (i : ι) => R) i) M ((fun (i : ι) => R) i) _inst_1 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) _inst_5 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_1 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (IsScalarTower.left.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R 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(x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u1, 0, max (max u2 u3) u1, max (max u2 u3) u1} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (SemilinearMapClass.distribMulActionHomClass.{0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => 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(x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) 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 Case conversion may be inaccurate. Consider using '#align fintype.linear_independent_iff' Fintype.linearIndependent_iff'ₓ'. -/
 /-- A finite family of vectors `v i` is linear independent iff the linear map that sends
 `c : ι → R` to `∑ i, c i • v i` has the trivial kernel. -/
@@ -286,10 +283,7 @@ theorem LinearIndependent.coe_range (i : LinearIndependent R v) :
 #align linear_independent.coe_range LinearIndependent.coe_range
 
 /- warning: linear_independent.map -> LinearIndependent.map is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align linear_independent.map LinearIndependent.mapₓ'. -/
 /-- If `v` is a linearly independent family of vectors and the kernel of a linear map `f` is
 disjoint with the submodule spanned by the vectors of `v`, then `f ∘ v` is a linearly independent
@@ -309,10 +303,7 @@ theorem LinearIndependent.map (hv : LinearIndependent R v) {f : M →ₗ[R] M'}
 #align linear_independent.map LinearIndependent.map
 
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 Case conversion may be inaccurate. Consider using '#align linear_independent.map' LinearIndependent.map'ₓ'. -/
 /-- An injective linear map sends linearly independent families of vectors to linearly independent
 families of vectors. See also `linear_independent.map` for a more general statement. -/
@@ -322,10 +313,7 @@ theorem LinearIndependent.map' (hv : LinearIndependent R v) (f : M →ₗ[R] M')
 #align linear_independent.map' LinearIndependent.map'
 
 /- warning: linear_independent.of_comp -> LinearIndependent.of_comp is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align linear_independent.of_comp LinearIndependent.of_compₓ'. -/
 /-- If the image of a family of vectors under a linear map is linearly independent, then so is
 the original family. -/
@@ -338,10 +326,7 @@ theorem LinearIndependent.of_comp (f : M →ₗ[R] M') (hfv : LinearIndependent
 #align linear_independent.of_comp LinearIndependent.of_comp
 
 /- warning: linear_map.linear_independent_iff -> LinearMap.linearIndependent_iff is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align linear_map.linear_independent_iff LinearMap.linearIndependent_iffₓ'. -/
 /-- If `f` is an injective linear map, then the family `f ∘ v` is linearly independent
 if and only if the family `v` is linearly independent. -/
@@ -414,10 +399,7 @@ theorem linearIndependent_span (hs : LinearIndependent R v) :
 #align linear_independent_span linearIndependent_span
 
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 Case conversion may be inaccurate. Consider using '#align linear_independent.fin_cons' LinearIndependent.fin_cons'ₓ'. -/
 /-- See `linear_independent.fin_cons` for a family of elements in a vector space. -/
 theorem LinearIndependent.fin_cons' {m : ℕ} (x : M) (v : Fin m → M) (hli : LinearIndependent R v)
@@ -504,10 +486,7 @@ section Subtype
 
 
 /- warning: linear_independent_comp_subtype -> linearIndependent_comp_subtype is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align linear_independent_comp_subtype linearIndependent_comp_subtypeₓ'. -/
 theorem linearIndependent_comp_subtype {s : Set ι} :
     LinearIndependent R (v ∘ coe : s → M) ↔
@@ -529,10 +508,7 @@ theorem linearIndependent_comp_subtype {s : Set ι} :
 #align linear_independent_comp_subtype linearIndependent_comp_subtype
 
 /- warning: linear_dependent_comp_subtype' -> linearDependent_comp_subtype' is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align linear_dependent_comp_subtype' linearDependent_comp_subtype'ₓ'. -/
 theorem linearDependent_comp_subtype' {s : Set ι} :
     ¬LinearIndependent R (v ∘ coe : s → M) ↔
@@ -541,10 +517,7 @@ theorem linearDependent_comp_subtype' {s : Set ι} :
 #align linear_dependent_comp_subtype' linearDependent_comp_subtype'
 
 /- warning: linear_dependent_comp_subtype -> linearDependent_comp_subtype is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align linear_dependent_comp_subtype linearDependent_comp_subtypeₓ'. -/
 /-- A version of `linear_dependent_comp_subtype'` with `finsupp.total` unfolded. -/
 theorem linearDependent_comp_subtype {s : Set ι} :
@@ -554,10 +527,7 @@ theorem linearDependent_comp_subtype {s : Set ι} :
 #align linear_dependent_comp_subtype linearDependent_comp_subtype
 
 /- warning: linear_independent_subtype -> linearIndependent_subtype is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_independent_subtype linearIndependent_subtypeₓ'. -/
 theorem linearIndependent_subtype {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
@@ -566,10 +536,7 @@ theorem linearIndependent_subtype {s : Set M} :
 #align linear_independent_subtype linearIndependent_subtype
 
 /- warning: linear_independent_comp_subtype_disjoint -> linearIndependent_comp_subtype_disjoint is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_independent_comp_subtype_disjoint linearIndependent_comp_subtype_disjointₓ'. -/
 theorem linearIndependent_comp_subtype_disjoint {s : Set ι} :
     LinearIndependent R (v ∘ coe : s → M) ↔
@@ -578,10 +545,7 @@ theorem linearIndependent_comp_subtype_disjoint {s : Set ι} :
 #align linear_independent_comp_subtype_disjoint linearIndependent_comp_subtype_disjoint
 
 /- warning: linear_independent_subtype_disjoint -> linearIndependent_subtype_disjoint is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_independent_subtype_disjoint linearIndependent_subtype_disjointₓ'. -/
 theorem linearIndependent_subtype_disjoint {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
@@ -590,10 +554,7 @@ theorem linearIndependent_subtype_disjoint {s : Set M} :
 #align linear_independent_subtype_disjoint linearIndependent_subtype_disjoint
 
 /- warning: linear_independent_iff_total_on -> linearIndependent_iff_totalOn is a dubious translation:
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Membership.mem.{max u2 u1, max u2 u1} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.setLike.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) x (Finsupp.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))) _inst_1 (Submodule.addCommMonoid.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.module.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_independent_iff_total_on linearIndependent_iff_totalOnₓ'. -/
 theorem linearIndependent_iff_totalOn {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔ (Finsupp.totalOn M M R id s).ker = ⊥ := by
@@ -787,10 +748,7 @@ theorem LinearIndependent.image {ι} {s : Set ι} {f : ι → M}
 #align linear_independent.image LinearIndependent.image
 
 /- warning: linear_independent.group_smul -> LinearIndependent.group_smul is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {G : Type.{u4}} [hG : Group.{u4} G] [_inst_8 : DistribMulAction.{u4, u2} G R (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1))))] [_inst_9 : DistribMulAction.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))] [_inst_10 : IsScalarTower.{u4, u2, u3} G R M (SMulZeroClass.toHasSmul.{u4, u2} G R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1)))))) (DistribSMul.toSmulZeroClass.{u4, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{u4, u2} G R (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1)))) _inst_8))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)))) (SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u4, u2, u3} G R M (SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u1, u2, u3} ι R M (SMul.smul.{max u1 u4, max u1 u3} (ι -> G) (ι -> M) (Pi.smul'.{u1, u4, u3} ι (fun (ᾰ : ι) => G) (fun (ᾰ : ι) => M) (fun (i : ι) => SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9)))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)
-but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {G : Type.{u3}} [hG : Group.{u3} G] [_inst_8 : DistribMulAction.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))] [_inst_9 : DistribMulAction.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))] [_inst_10 : IsScalarTower.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u2} G R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (DistribSMul.toSMulZeroClass.{u3, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))) (DistribMulAction.toDistribSMul.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1))) _inst_8))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u4, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u4, u2, u1} ι R M (HSMul.hSMul.{max u4 u3, max u4 u1, max u4 u1} (ι -> G) (ι -> M) (ι -> M) (instHSMul.{max u4 u3, max u4 u1} (ι -> G) (ι -> M) (Pi.smul'.{u4, u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6779 : ι) => G) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6773 : ι) => M) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_independent.group_smul LinearIndependent.group_smulₓ'. -/
 theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulAction G R]
     [DistribMulAction G M] [IsScalarTower G R M] [SMulCommClass G R M] {v : ι → M}
@@ -941,10 +899,7 @@ theorem LinearIndependent.not_mem_span_image [Nontrivial R] (hv : LinearIndepend
 #align linear_independent.not_mem_span_image LinearIndependent.not_mem_span_image
 
 /- warning: linear_independent.total_ne_of_not_mem_support -> LinearIndependent.total_ne_of_not_mem_support is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align linear_independent.total_ne_of_not_mem_support LinearIndependent.total_ne_of_not_mem_supportₓ'. -/
 theorem LinearIndependent.total_ne_of_not_mem_support [Nontrivial R] (hv : LinearIndependent R v)
     {x : ι} (f : ι →₀ R) (h : x ∉ f.support) : Finsupp.total ι M R v f ≠ v x :=
@@ -1132,10 +1087,7 @@ def LinearIndependent.repr (hv : LinearIndependent R v) : span R (range v) →
 #align linear_independent.repr LinearIndependent.repr
 
 /- warning: linear_independent.total_repr -> LinearIndependent.total_repr is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_independent.total_repr LinearIndependent.total_reprₓ'. -/
 @[simp]
 theorem LinearIndependent.total_repr (x) : Finsupp.total ι M R v (hv.repr x) = x :=
@@ -1143,10 +1095,7 @@ theorem LinearIndependent.total_repr (x) : Finsupp.total ι M R v (hv.repr x) =
 #align linear_independent.total_repr LinearIndependent.total_repr
 
 /- warning: linear_independent.total_comp_repr -> LinearIndependent.total_comp_repr is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_independent.total_comp_repr LinearIndependent.total_comp_reprₓ'. -/
 theorem LinearIndependent.total_comp_repr :
     (Finsupp.total ι M R v).comp hv.repr = Submodule.subtype _ :=
@@ -1154,30 +1103,21 @@ theorem LinearIndependent.total_comp_repr :
 #align linear_independent.total_comp_repr LinearIndependent.total_comp_repr
 
 /- warning: linear_independent.repr_ker -> LinearIndependent.repr_ker is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_ker LinearIndependent.repr_kerₓ'. -/
 theorem LinearIndependent.repr_ker : hv.repr.ker = ⊥ := by
   rw [LinearIndependent.repr, LinearEquiv.ker]
 #align linear_independent.repr_ker LinearIndependent.repr_ker
 
 /- warning: linear_independent.repr_range -> LinearIndependent.repr_range is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_range LinearIndependent.repr_rangeₓ'. -/
 theorem LinearIndependent.repr_range : hv.repr.range = ⊤ := by
   rw [LinearIndependent.repr, LinearEquiv.range]
 #align linear_independent.repr_range LinearIndependent.repr_range
 
 /- warning: linear_independent.repr_eq -> LinearIndependent.repr_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq LinearIndependent.repr_eqₓ'. -/
 theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M R v l = ↑x) :
     hv.repr x = l :=
@@ -1196,10 +1136,7 @@ theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M
 #align linear_independent.repr_eq LinearIndependent.repr_eq
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq_single LinearIndependent.repr_eq_singleₓ'. -/
 theorem LinearIndependent.repr_eq_single (i) (x) (hx : ↑x = v i) : hv.repr x = Finsupp.single i 1 :=
   by
@@ -1208,10 +1145,7 @@ theorem LinearIndependent.repr_eq_single (i) (x) (hx : ↑x = v i) : hv.repr x =
 #align linear_independent.repr_eq_single LinearIndependent.repr_eq_single
 
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 Case conversion may be inaccurate. Consider using '#align linear_independent.span_repr_eq LinearIndependent.span_repr_eqₓ'. -/
 theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
     Span.repr R (Set.range v) x = (hv.repr x).equivMapDomain (Equiv.ofInjective _ hv.Injective) :=
@@ -1282,10 +1216,7 @@ theorem LinearIndependent.independent_span_singleton (hv : LinearIndependent R v
 variable (R)
 
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 Case conversion may be inaccurate. Consider using '#align exists_maximal_independent' exists_maximal_independent'ₓ'. -/
 theorem exists_maximal_independent' (s : ι → M) :
     ∃ I : Set ι,
@@ -1315,10 +1246,7 @@ theorem exists_maximal_independent' (s : ι → M) :
 #align exists_maximal_independent' exists_maximal_independent'
 
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 Case conversion may be inaccurate. Consider using '#align exists_maximal_independent exists_maximal_independentₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » I) -/
 theorem exists_maximal_independent (s : ι → M) :
@@ -1415,10 +1343,7 @@ theorem eq_of_linearIndependent_of_span_subtype [Nontrivial R] {s t : Set M}
 open LinearMap
 
 /- warning: linear_independent.image_subtype -> LinearIndependent.image_subtype is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align linear_independent.image_subtype LinearIndependent.image_subtypeₓ'. -/
 theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
     (hs : LinearIndependent R (fun x => x : s → M)) (hf_inj : Disjoint (span R s) f.ker) :
@@ -1430,10 +1355,7 @@ theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
 #align linear_independent.image_subtype LinearIndependent.image_subtype
 
 /- warning: linear_independent.inl_union_inr -> LinearIndependent.inl_union_inr is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align linear_independent.inl_union_inr LinearIndependent.inl_union_inrₓ'. -/
 theorem LinearIndependent.inl_union_inr {s : Set M} {t : Set M'}
     (hs : LinearIndependent R (fun x => x : s → M))
@@ -1446,10 +1368,7 @@ theorem LinearIndependent.inl_union_inr {s : Set M} {t : Set M'}
 #align linear_independent.inl_union_inr LinearIndependent.inl_union_inr
 
 /- warning: linear_independent_inl_union_inr' -> linearIndependent_inl_union_inr' is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align linear_independent_inl_union_inr' linearIndependent_inl_union_inr'ₓ'. -/
 theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv : LinearIndependent R v)
     (hv' : LinearIndependent R v') :
@@ -1748,10 +1667,7 @@ theorem linearIndependent_option {v : Option ι → V} :
 #align linear_independent_option linearIndependent_option
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_independent_insert' linearIndependent_insert'ₓ'. -/
 theorem linearIndependent_insert' {ι} {s : Set ι} {a : ι} {f : ι → V} (has : a ∉ s) :
     (LinearIndependent K fun x : insert a s => f x) ↔

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -116,7 +116,7 @@ variable {R} {v}
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2], Iff (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), (Eq.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u3, u2} ι M R _inst_1 _inst_2 _inst_5 v) l) (OfNat.ofNat.{u3} M 0 (OfNat.mk.{u3} M 0 (Zero.zero.{u3} M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2))))))) -> (Eq.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) l (OfNat.ofNat.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) 0 (OfNat.mk.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) 0 (Zero.zero.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Finsupp.zero.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.zero.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.zero.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_iff linearIndependent_iffₓ'. -/
 theorem linearIndependent_iff : LinearIndependent R v ↔ ∀ l, Finsupp.total ι M R v l = 0 → l = 0 :=
   by simp [LinearIndependent, LinearMap.ker_eq_bot']
@@ -207,7 +207,7 @@ theorem Fintype.linearIndependent_iff [Fintype ι] :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] [_inst_8 : Fintype.{u1} ι], Iff (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5) (Eq.{succ (max u1 u2)} (Submodule.{u2, max u1 u2} R (forall (i : ι), (fun (i : ι) => R) i) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i))) (LinearMap.ker.{u2, u2, max u1 u2, u3, max (max u1 u2) u3} R R (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) 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(Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (coeFn.{max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3)), max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3))} (LinearEquiv.{0, 0, max u1 u2 u3, max (max u1 u2) u3} Nat Nat Nat.semiring Nat.semiring 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_inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.module.{u2, u2, 0, u2, u3} R R Nat ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.module.{u2, u2, 0, max u1 u2, u3} R R Nat (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) => (forall (i : ι), LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) -> (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (forall (i : ι), (fun (i : ι) => R) i) M (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5)) (LinearEquiv.hasCoeToFun.{0, 0, max u1 u2 u3, max (max u1 u2) u3} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (forall (i : ι), (fun (i : ι) => R) i) M (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, max u2 u3} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u1 u2, u3} R R (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u1, max u2 u3, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.module.{u2, u2, 0, u2, u3} R R Nat ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.module.{u2, u2, 0, max u1 u2, u3} R R Nat (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)) (LinearMap.lsum.{u2, u3, u1, u2, 0} R M ι _inst_1 (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) Nat _inst_2 _inst_5 _inst_8 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u1} ι a b)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5))) (fun (i : ι) => LinearMap.smulRight.{u2, u2, u3, u2} R ((fun (i : ι) => R) i) M ((fun (i : ι) => R) i) _inst_1 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) _inst_5 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_1 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (IsScalarTower.left.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2))) (Module.toMulActionWithZero.{u2, u3} R M _inst_1 _inst_2 _inst_5))) (LinearMap.id.{u2, u2} R ((fun (i : ι) => R) i) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) (v i)))) (Bot.bot.{max u1 u2} (Submodule.{u2, max u1 u2} R (forall (i : ι), (fun (i : ι) => R) i) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i))) (Submodule.hasBot.{u2, max u1 u2} R (forall (i : ι), (fun (i : ι) => R) i) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] [_inst_8 : Fintype.{u3} ι], Iff (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) (Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.ker.{u2, u2, max u3 u2, u1, max (max u3 u2) u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun 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(Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) 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(x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u1, 0, max (max u2 u3) u1, max (max u2 u3) u1} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (SemilinearMapClass.distribMulActionHomClass.{0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (LinearMap.lsum.{u2, u1, u3, u2, 0} R M ι _inst_1 (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) Nat _inst_2 _inst_5 _inst_8 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u3} ι a b)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (fun (i : ι) => LinearMap.smulRight.{u2, u2, u1, u2} R R M R _inst_1 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) _inst_5 (Semiring.toModule.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R _inst_1) _inst_5 (IsScalarTower.left.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (LinearMap.id.{u2, u2} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (v i)))) (Bot.bot.{max u3 u2} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (Submodule.instBotSubmodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] [_inst_8 : Fintype.{u3} ι], Iff (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) (Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.ker.{u2, u2, max u3 u2, u1, max (max u3 u2) u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun 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(Semiring.toModule.{u2} R _inst_1)) (v i))) (LinearMap.semilinearMapClass.{u2, u2, max u3 u2, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (max (succ u2) (succ u3)) (succ u1), max (max (succ u2) (succ u3)) (succ u1)} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) 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(x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) 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(x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (_x : forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) _x) (SMulHomClass.toFunLike.{max (max u2 u3) u1, 0, max (max u2 u3) u1, max (max u2 u3) u1} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u1, 0, max (max u2 u3) u1, max (max u2 u3) u1} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (SemilinearMapClass.distribMulActionHomClass.{0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (LinearMap.lsum.{u2, u1, u3, u2, 0} R M ι _inst_1 (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) Nat _inst_2 _inst_5 _inst_8 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u3} ι a b)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (fun (i : ι) => LinearMap.smulRight.{u2, u2, u1, u2} R R M R _inst_1 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) _inst_5 (Semiring.toModule.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R _inst_1) _inst_5 (IsScalarTower.left.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (LinearMap.id.{u2, u2} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (v i)))) (Bot.bot.{max u3 u2} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (Submodule.instBotSubmodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align fintype.linear_independent_iff' Fintype.linearIndependent_iff'ₓ'. -/
 /-- A finite family of vectors `v i` is linear independent iff the linear map that sends
 `c : ι → R` to `∑ i, c i • v i` has the trivial kernel. -/
@@ -289,7 +289,7 @@ theorem LinearIndependent.coe_range (i : LinearIndependent R v) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {M' : Type.{u4}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u4} M'] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] [_inst_6 : Module.{u2, u4} R M' _inst_1 _inst_3], (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5) -> (forall {f : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6}, (Disjoint.{u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (SetLike.partialOrder.{u3, u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u2, u3} R M _inst_1 _inst_2 _inst_5)) (Submodule.orderBot.{u2, u3} R M _inst_1 _inst_2 _inst_5) (Submodule.span.{u2, u3} R M _inst_1 _inst_2 _inst_5 (Set.range.{u3, succ u1} M ι v)) (LinearMap.ker.{u2, u2, u3, u4, max u3 u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)) -> (LinearIndependent.{u1, u2, u4} ι R M' (Function.comp.{succ u1, succ u3, succ u4} ι M M' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
 but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3], (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5) -> (forall {f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6}, (Disjoint.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.completeLattice.{u3, u2} R M _inst_1 _inst_2 _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.span.{u3, u2} R M _inst_1 _inst_2 _inst_5 (Set.range.{u2, succ u4} M ι v)) (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
+  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3], (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5) -> (forall {f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6}, (Disjoint.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.completeLattice.{u3, u2} R M _inst_1 _inst_2 _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.span.{u3, u2} R M _inst_1 _inst_2 _inst_5 (Set.range.{u2, succ u4} M ι v)) (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
 Case conversion may be inaccurate. Consider using '#align linear_independent.map LinearIndependent.mapₓ'. -/
 /-- If `v` is a linearly independent family of vectors and the kernel of a linear map `f` is
 disjoint with the submodule spanned by the vectors of `v`, then `f ∘ v` is a linearly independent
@@ -312,7 +312,7 @@ theorem LinearIndependent.map (hv : LinearIndependent R v) {f : M →ₗ[R] M'}
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {M' : Type.{u4}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u4} M'] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] [_inst_6 : Module.{u2, u4} R M' _inst_1 _inst_3], (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5) -> (forall (f : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (Eq.{succ u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (LinearMap.ker.{u2, u2, u3, u4, max u3 u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (Bot.bot.{u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (Submodule.hasBot.{u2, u3} R M _inst_1 _inst_2 _inst_5))) -> (LinearIndependent.{u1, u2, u4} ι R M' (Function.comp.{succ u1, succ u3, succ u4} ι M M' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
 but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3], (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5) -> (forall (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) (Bot.bot.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.instBotSubmodule.{u3, u2} R M _inst_1 _inst_2 _inst_5))) -> (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
+  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3], (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5) -> (forall (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) (Bot.bot.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.instBotSubmodule.{u3, u2} R M _inst_1 _inst_2 _inst_5))) -> (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
 Case conversion may be inaccurate. Consider using '#align linear_independent.map' LinearIndependent.map'ₓ'. -/
 /-- An injective linear map sends linearly independent families of vectors to linearly independent
 families of vectors. See also `linear_independent.map` for a more general statement. -/
@@ -325,7 +325,7 @@ theorem LinearIndependent.map' (hv : LinearIndependent R v) (f : M →ₗ[R] M')
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {M' : Type.{u4}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u4} M'] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] [_inst_6 : Module.{u2, u4} R M' _inst_1 _inst_3] (f : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (LinearIndependent.{u1, u2, u4} ι R M' (Function.comp.{succ u1, succ u3, succ u4} ι M M' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6) -> (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5)
 but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6) -> (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5)
+  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6) -> (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent.of_comp LinearIndependent.of_compₓ'. -/
 /-- If the image of a family of vectors under a linear map is linearly independent, then so is
 the original family. -/
@@ -341,7 +341,7 @@ theorem LinearIndependent.of_comp (f : M →ₗ[R] M') (hfv : LinearIndependent
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {M' : Type.{u4}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u4} M'] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] [_inst_6 : Module.{u2, u4} R M' _inst_1 _inst_3] (f : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (Eq.{succ u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (LinearMap.ker.{u2, u2, u3, u4, max u3 u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (Bot.bot.{u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (Submodule.hasBot.{u2, u3} R M _inst_1 _inst_2 _inst_5))) -> (Iff (LinearIndependent.{u1, u2, u4} ι R M' (Function.comp.{succ u1, succ u3, succ u4} ι M M' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6) (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5))
 but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) (Bot.bot.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.instBotSubmodule.{u3, u2} R M _inst_1 _inst_2 _inst_5))) -> (Iff (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6) (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5))
+  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) (Bot.bot.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.instBotSubmodule.{u3, u2} R M _inst_1 _inst_2 _inst_5))) -> (Iff (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6) (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5))
 Case conversion may be inaccurate. Consider using '#align linear_map.linear_independent_iff LinearMap.linearIndependent_iffₓ'. -/
 /-- If `f` is an injective linear map, then the family `f ∘ v` is linearly independent
 if and only if the family `v` is linearly independent. -/
@@ -507,7 +507,7 @@ section Subtype
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] {s : Set.{u1} ι}, Iff (LinearIndependent.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) R M (Function.comp.{succ u1, succ u1, succ u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι M v ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeSubtype.{succ u1} ι (fun (x : ι) => Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) x s))))))) _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), (Membership.Mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Submodule.setLike.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) l (Finsupp.supported.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s)) -> (Eq.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u3, u2} ι M R _inst_1 _inst_2 _inst_5 v) l) (OfNat.ofNat.{u3} M 0 (OfNat.mk.{u3} M 0 (Zero.zero.{u3} M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2))))))) -> (Eq.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) l (OfNat.ofNat.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) 0 (OfNat.mk.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) 0 (Zero.zero.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Finsupp.zero.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))))
 but is expected to have type
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_inst_1))) => M) l) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) l (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R 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+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, Iff (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))), (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) l (Finsupp.supported.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R 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_inst_1))) => M) l) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) l (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (Finsupp.zero.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_comp_subtype linearIndependent_comp_subtypeₓ'. -/
 theorem linearIndependent_comp_subtype {s : Set ι} :
     LinearIndependent R (v ∘ coe : s → M) ↔
@@ -532,7 +532,7 @@ theorem linearIndependent_comp_subtype {s : Set ι} :
 lean 3 declaration is
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 but is expected to have type
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(Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v) f) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) _inst_2))))) (Ne.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) f (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.zero.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, Iff (Not (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5)) (Exists.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (f : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => And (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (Submodule.setLike.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) f (Finsupp.supported.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s)) (And (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v) f) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) _inst_2))))) (Ne.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) f (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.zero.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))))))
 Case conversion may be inaccurate. Consider using '#align linear_dependent_comp_subtype' linearDependent_comp_subtype'ₓ'. -/
 theorem linearDependent_comp_subtype' {s : Set ι} :
     ¬LinearIndependent R (v ∘ coe : s → M) ↔
@@ -557,7 +557,7 @@ theorem linearDependent_comp_subtype {s : Set ι} :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x s))))) x) _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))), (Membership.Mem.{max u2 u1, max u2 u1} (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Submodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R 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_inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) (Submodule.setLike.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) -> (Eq.{succ u2} M (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) (fun (_x : LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) => (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u2} R R (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_2 _inst_5 (id.{succ u2} M)) l) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))))) -> (Eq.{max (succ u2) (succ u1)} (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) l (OfNat.ofNat.{max u2 u1} (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) 0 (OfNat.mk.{max u2 u1} (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) 0 (Zero.zero.{max u2 u1} (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Finsupp.zero.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M s) R M (fun (x : Set.Elem.{u2} M s) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) x) _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))), (Membership.mem.{max u1 u2, max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.setLike.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_2 _inst_5 (id.{succ u2} M)) l) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u1) (succ u2)} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) l (OfNat.ofNat.{max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) 0 (Zero.toOfNat0.{max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Finsupp.zero.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M s) R M (fun (x : Set.Elem.{u2} M s) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) x) _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))), (Membership.mem.{max u1 u2, max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.setLike.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_2 _inst_5 (id.{succ u2} M)) l) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u1) (succ u2)} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) l (OfNat.ofNat.{max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) 0 (Zero.toOfNat0.{max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Finsupp.zero.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_subtype linearIndependent_subtypeₓ'. -/
 theorem linearIndependent_subtype {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
@@ -699,7 +699,7 @@ variable {a b : R} {x y : M}
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], Iff (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Function.Injective.{max (succ u1) (succ u2), succ u3} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u1, u3, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 v)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], Iff (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Function.Injective.{max (succ u3) (succ u2), succ u1} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v)))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], Iff (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Function.Injective.{max (succ u3) (succ u2), succ u1} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v)))
 Case conversion may be inaccurate. Consider using '#align linear_independent_iff_injective_total linearIndependent_iff_injective_totalₓ'. -/
 theorem linearIndependent_iff_injective_total :
     LinearIndependent R v ↔ Function.Injective (Finsupp.total ι M R v) :=
@@ -711,7 +711,7 @@ theorem linearIndependent_iff_injective_total :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (Function.Injective.{max (succ u1) (succ u2), succ u3} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u1, u3, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 v)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (Function.Injective.{max (succ u3) (succ u2), succ u1} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v)))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (Function.Injective.{max (succ u3) (succ u2), succ u1} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v)))
 Case conversion may be inaccurate. Consider using '#align linear_independent.injective_total LinearIndependent.injective_totalₓ'. -/
 alias linearIndependent_iff_injective_total ↔ LinearIndependent.injective_total _
 #align linear_independent.injective_total LinearIndependent.injective_total
@@ -944,7 +944,7 @@ theorem LinearIndependent.not_mem_span_image [Nontrivial R] (hv : LinearIndepend
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_8 : Nontrivial.{u2} R], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall {x : ι} (f : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))), (Not (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) x (Finsupp.support.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) f))) -> (Ne.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u1, u3, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 v) f) (v x)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Nontrivial.{u2} R], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall {x : ι} (f : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))), (Not (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) x (Finsupp.support.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) f))) -> (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) f) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v) f) (v x)))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Nontrivial.{u2} R], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall {x : ι} (f : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))), (Not (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) x (Finsupp.support.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) f))) -> (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) f) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v) f) (v x)))
 Case conversion may be inaccurate. Consider using '#align linear_independent.total_ne_of_not_mem_support LinearIndependent.total_ne_of_not_mem_supportₓ'. -/
 theorem LinearIndependent.total_ne_of_not_mem_support [Nontrivial R] (hv : LinearIndependent R v)
     {x : ι} (f : ι →₀ R) (h : x ∉ f.support) : Finsupp.total ι M R v f ≠ v x :=
@@ -1135,7 +1135,7 @@ def LinearIndependent.repr (hv : LinearIndependent R v) : span R (range v) →
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))), Eq.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ 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(Ring.toSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align linear_independent.total_repr LinearIndependent.total_reprₓ'. -/
 @[simp]
 theorem LinearIndependent.total_repr (x) : Finsupp.total ι M R v (hv.repr x) = x :=
@@ -1177,7 +1177,7 @@ theorem LinearIndependent.repr_range : hv.repr.range = ⊤ := by
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) {l : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))} {x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) 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u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) -> (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R 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(NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv) x) l)
 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq LinearIndependent.repr_eqₓ'. -/
 theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M R v l = ↑x) :
     hv.repr x = l :=
@@ -1199,7 +1199,7 @@ theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (i : ι) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))), (Eq.{succ u3} M ((fun (a : Type.{u3}) (b : 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(Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) 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(AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1)))))))))
 but is expected to have type
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(Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv) x) (Finsupp.single.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) i (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (i : ι) (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))), (Eq.{succ u2} M 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x 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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv) x) (Finsupp.single.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) i (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq_single LinearIndependent.repr_eq_singleₓ'. -/
 theorem LinearIndependent.repr_eq_single (i) (x) (hx : ↑x = v i) : hv.repr x = Finsupp.single i 1 :=
   by
@@ -1211,7 +1211,7 @@ theorem LinearIndependent.repr_eq_single (i) (x) (hx : ↑x = v i) : hv.repr x =
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) [_inst_8 : Nontrivial.{u2} R] (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))), Eq.{max (succ u3) 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(NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv) x))
 but is expected to have type
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(fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) [_inst_8 : Nontrivial.{u2} R] (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι 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(fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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 Case conversion may be inaccurate. Consider using '#align linear_independent.span_repr_eq LinearIndependent.span_repr_eqₓ'. -/
 theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
     Span.repr R (Set.range v) x = (hv.repr x).equivMapDomain (Equiv.ofInjective _ hv.Injective) :=
@@ -1418,7 +1418,7 @@ open LinearMap
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {M' : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3)] {s : Set.{u2} M} {f : LinearMap.{u1, u1, u2, u3} 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))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6}, (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => 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(Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) s)) M' (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M') Type.{u3} (Set.hasCoeToSort.{u3} M') (Set.image.{u2, u3} M M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} 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))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} 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))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) 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(AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) s)))))) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_6)
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u3}} {M' : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_6 : Module.{u2, u1} R M' (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)] {s : Set.{u3} M} {f : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6}, (LinearIndependent.{u3, u2, u3} (Set.Elem.{u3} M s) R M (fun (x : Set.Elem.{u3} M s) => Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x s) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (Disjoint.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 s) (LinearMap.ker.{u2, u2, u3, u1, max u3 u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (LinearIndependent.{u1, u2, u1} (Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) R M' (fun (x : Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) => Subtype.val.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Set.{u1} M') (Set.instMembershipSet.{u1} M') x (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') a) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_6)
+  forall {R : Type.{u2}} {M : Type.{u3}} {M' : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_6 : Module.{u2, u1} R M' (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)] {s : Set.{u3} M} {f : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6}, (LinearIndependent.{u3, u2, u3} (Set.Elem.{u3} M s) R M (fun (x : Set.Elem.{u3} M s) => Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x s) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (Disjoint.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 s) (LinearMap.ker.{u2, u2, u3, u1, max u3 u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (LinearIndependent.{u1, u2, u1} (Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) R M' (fun (x : Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) => Subtype.val.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Set.{u1} M') (Set.instMembershipSet.{u1} M') x (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') a) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_6)
 Case conversion may be inaccurate. Consider using '#align linear_independent.image_subtype LinearIndependent.image_subtypeₓ'. -/
 theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
     (hs : LinearIndependent R (fun x => x : s → M)) (hf_inj : Disjoint (span R s) f.ker) :
@@ -1433,14 +1433,14 @@ theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
 lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u2} M' _inst_3)) _inst_6 (Prod.module.{u1, u3, u2} R M M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.inr.{u1, u3, u2} R M M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_3) _inst_5 _inst_6)) t))) x) (Ring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u3, u2} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_3)) (Prod.module.{u1, u3, u2} R M M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_3) _inst_5 _inst_6))
 Case conversion may be inaccurate. Consider using '#align linear_independent.inl_union_inr LinearIndependent.inl_union_inrₓ'. -/
 theorem LinearIndependent.inl_union_inr {s : Set M} {t : Set M'}
     (hs : LinearIndependent R (fun x => x : s → M))
     (ht : LinearIndependent R (fun x => x : t → M')) :
     LinearIndependent R (fun x => x : inl R M M' '' s ∪ inr R M M' '' t → M × M') :=
   by
-  refine' (hs.image_subtype _).union (ht.image_subtype _) _ <;> [simp, simp, skip]
+  refine' (hs.image_subtype _).union (ht.image_subtype _) _ <;> [simp;simp;skip]
   simp only [span_image]
   simp [disjoint_iff, prod_inf_prod]
 #align linear_independent.inl_union_inr LinearIndependent.inl_union_inr
@@ -1449,7 +1449,7 @@ theorem LinearIndependent.inl_union_inr {s : Set M} {t : Set M'}
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u4}} {M' : Type.{u5}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u4} M] [_inst_3 : AddCommGroup.{u5} M'] [_inst_5 : Module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] [_inst_6 : Module.{u3, u5} R M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)] {v : ι -> M} {v' : ι' -> M'}, (LinearIndependent.{u1, u3, u4} ι R M v (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5) -> (LinearIndependent.{u2, u3, u5} ι' R M' v' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_6) -> (LinearIndependent.{max u1 u2, u3, max u4 u5} (Sum.{u1, u2} ι ι') R (Prod.{u4, u5} M M') (Sum.elim.{u1, u2, succ (max u4 u5)} ι ι' (Prod.{u4, u5} M M') (Function.comp.{succ u1, succ u4, succ (max u4 u5)} ι M (Prod.{u4, u5} M M') (coeFn.{max (succ u4) (succ (max u4 u5)), max (succ u4) (succ (max u4 u5))} (LinearMap.{u3, u3, u4, max u4 u5} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M (Prod.{u4, u5} M M') (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (Prod.addCommMonoid.{u4, u5} M M' (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)) _inst_5 (Prod.module.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6)) (fun (_x : LinearMap.{u3, u3, u4, max u4 u5} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M (Prod.{u4, u5} M M') (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (Prod.addCommMonoid.{u4, u5} M M' (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)) _inst_5 (Prod.module.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6)) => M -> (Prod.{u4, u5} M M')) (LinearMap.hasCoeToFun.{u3, u3, u4, max u4 u5} R R M (Prod.{u4, u5} M M') (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (Prod.addCommMonoid.{u4, u5} M M' (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)) _inst_5 (Prod.module.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (LinearMap.inl.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6)) v) (Function.comp.{succ u2, succ u5, max (succ u4) (succ u5)} ι' M' (Prod.{u4, u5} M M') (coeFn.{max (succ u5) (succ (max u4 u5)), max (succ u5) (succ (max u4 u5))} (LinearMap.{u3, u3, u5, max u4 u5} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M' (Prod.{u4, u5} M M') (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) (Prod.addCommMonoid.{u4, u5} M M' (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)) _inst_6 (Prod.module.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6)) (fun (_x : LinearMap.{u3, u3, u5, max u4 u5} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M' (Prod.{u4, u5} M M') (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) (Prod.addCommMonoid.{u4, u5} M M' (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)) _inst_6 (Prod.module.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6)) => M' -> (Prod.{u4, u5} M M')) (LinearMap.hasCoeToFun.{u3, u3, u5, max u4 u5} R R M' (Prod.{u4, u5} M M') (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) (Prod.addCommMonoid.{u4, u5} M M' (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)) _inst_6 (Prod.module.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (LinearMap.inr.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6)) v')) (Ring.toSemiring.{u3} R _inst_1) (Prod.addCommMonoid.{u4, u5} M M' (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)) (Prod.module.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6))
 but is expected to have type
-  forall {ι : Type.{u5}} {ι' : Type.{u2}} {R : Type.{u4}} {M : Type.{u3}} {M' : Type.{u1}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_6 : Module.{u4, u1} R M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)] {v : ι -> M} {v' : ι' -> M'}, (LinearIndependent.{u5, u4, u3} ι R M v (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearIndependent.{u2, u4, u1} ι' R M' v' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_6) -> (LinearIndependent.{max u2 u5, u4, max u3 u1} (Sum.{u5, u2} ι ι') R (Prod.{u3, u1} M M') (Sum.elim.{u5, u2, succ (max u3 u1)} ι ι' (Prod.{u3, u1} M M') (Function.comp.{succ u5, succ u3, succ (max u3 u1)} ι M (Prod.{u3, u1} M M') (FunLike.coe.{max (succ u3) (succ u1), succ u3, max (succ u3) (succ u1)} (LinearMap.{u4, u4, u3, max u1 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))) M (Prod.{u3, u1} M M') (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_5 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Prod.{u3, u1} M M') _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u3 u1} R R M (Prod.{u3, u1} M M') (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_5 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (LinearMap.inl.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) v) (Function.comp.{succ u2, succ u1, max (succ u3) (succ u1)} ι' M' (Prod.{u3, u1} M M') (FunLike.coe.{max (succ u3) (succ u1), succ u1, max (succ u3) (succ u1)} (LinearMap.{u4, u4, u1, max u1 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))) M' (Prod.{u3, u1} M M') (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_6 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) M' (fun (_x : M') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M') => Prod.{u3, u1} M M') _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, max u3 u1} R R M' (Prod.{u3, u1} M M') (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_6 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (LinearMap.inr.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) v')) (Ring.toSemiring.{u4} R _inst_1) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6))
+  forall {ι : Type.{u5}} {ι' : Type.{u2}} {R : Type.{u4}} {M : Type.{u3}} {M' : Type.{u1}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_6 : Module.{u4, u1} R M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)] {v : ι -> M} {v' : ι' -> M'}, (LinearIndependent.{u5, u4, u3} ι R M v (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearIndependent.{u2, u4, u1} ι' R M' v' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_6) -> (LinearIndependent.{max u2 u5, u4, max u3 u1} (Sum.{u5, u2} ι ι') R (Prod.{u3, u1} M M') (Sum.elim.{u5, u2, succ (max u3 u1)} ι ι' (Prod.{u3, u1} M M') (Function.comp.{succ u5, succ u3, succ (max u3 u1)} ι M (Prod.{u3, u1} M M') (FunLike.coe.{max (succ u3) (succ u1), succ u3, max (succ u3) (succ u1)} (LinearMap.{u4, u4, u3, max u1 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))) M (Prod.{u3, u1} M M') (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_5 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Prod.{u3, u1} M M') _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u3 u1} R R M (Prod.{u3, u1} M M') (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_5 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (LinearMap.inl.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) v) (Function.comp.{succ u2, succ u1, max (succ u3) (succ u1)} ι' M' (Prod.{u3, u1} M M') (FunLike.coe.{max (succ u3) (succ u1), succ u1, max (succ u3) (succ u1)} (LinearMap.{u4, u4, u1, max u1 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))) M' (Prod.{u3, u1} M M') (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_6 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) M' (fun (_x : M') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M') => Prod.{u3, u1} M M') _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, max u3 u1} R R M' (Prod.{u3, u1} M M') (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_6 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (LinearMap.inr.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) v')) (Ring.toSemiring.{u4} R _inst_1) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6))
 Case conversion may be inaccurate. Consider using '#align linear_independent_inl_union_inr' linearIndependent_inl_union_inr'ₓ'. -/
 theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv : LinearIndependent R v)
     (hv' : LinearIndependent R v') :

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -365,7 +365,7 @@ theorem linearIndependent_of_subsingleton [Subsingleton R] : LinearIndependent R
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u4}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_5 : Module.{u3, u4} R M _inst_1 _inst_2] (e : Equiv.{succ u1, succ u2} ι ι') {f : ι' -> M}, Iff (LinearIndependent.{u1, u3, u4} ι R M (Function.comp.{succ u1, succ u2, succ u4} ι ι' M f (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} ι ι') (fun (_x : Equiv.{succ u1, succ u2} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{succ u1, succ u2} ι ι') e)) _inst_1 _inst_2 _inst_5) (LinearIndependent.{u2, u3, u4} ι' R M f _inst_1 _inst_2 _inst_5)
 but is expected to have type
-  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] (e : Equiv.{succ u4, succ u3} ι ι') {f : ι' -> M}, Iff (LinearIndependent.{u4, u2, u1} ι R M (Function.comp.{succ u4, succ u3, succ u1} ι ι' M f (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} ι ι') e)) _inst_1 _inst_2 _inst_5) (LinearIndependent.{u3, u2, u1} ι' R M f _inst_1 _inst_2 _inst_5)
+  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] (e : Equiv.{succ u4, succ u3} ι ι') {f : ι' -> M}, Iff (LinearIndependent.{u4, u2, u1} ι R M (Function.comp.{succ u4, succ u3, succ u1} ι ι' M f (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} ι ι') e)) _inst_1 _inst_2 _inst_5) (LinearIndependent.{u3, u2, u1} ι' R M f _inst_1 _inst_2 _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent_equiv linearIndependent_equivₓ'. -/
 theorem linearIndependent_equiv (e : ι ≃ ι') {f : ι' → M} :
     LinearIndependent R (f ∘ e) ↔ LinearIndependent R f :=
@@ -377,7 +377,7 @@ theorem linearIndependent_equiv (e : ι ≃ ι') {f : ι' → M} :
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u4}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_5 : Module.{u3, u4} R M _inst_1 _inst_2] (e : Equiv.{succ u1, succ u2} ι ι') {f : ι' -> M} {g : ι -> M}, (Eq.{max (succ u1) (succ u4)} (ι -> M) (Function.comp.{succ u1, succ u2, succ u4} ι ι' M f (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} ι ι') (fun (_x : Equiv.{succ u1, succ u2} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{succ u1, succ u2} ι ι') e)) g) -> (Iff (LinearIndependent.{u1, u3, u4} ι R M g _inst_1 _inst_2 _inst_5) (LinearIndependent.{u2, u3, u4} ι' R M f _inst_1 _inst_2 _inst_5))
 but is expected to have type
-  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] (e : Equiv.{succ u4, succ u3} ι ι') {f : ι' -> M} {g : ι -> M}, (Eq.{max (succ u4) (succ u2)} (ι -> M) (Function.comp.{succ u4, succ u3, succ u2} ι ι' M f (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} ι ι') e)) g) -> (Iff (LinearIndependent.{u4, u1, u2} ι R M g _inst_1 _inst_2 _inst_5) (LinearIndependent.{u3, u1, u2} ι' R M f _inst_1 _inst_2 _inst_5))
+  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] (e : Equiv.{succ u4, succ u3} ι ι') {f : ι' -> M} {g : ι -> M}, (Eq.{max (succ u4) (succ u2)} (ι -> M) (Function.comp.{succ u4, succ u3, succ u2} ι ι' M f (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} ι ι') e)) g) -> (Iff (LinearIndependent.{u4, u1, u2} ι R M g _inst_1 _inst_2 _inst_5) (LinearIndependent.{u3, u1, u2} ι' R M f _inst_1 _inst_2 _inst_5))
 Case conversion may be inaccurate. Consider using '#align linear_independent_equiv' linearIndependent_equiv'ₓ'. -/
 theorem linearIndependent_equiv' (e : ι ≃ ι') {f : ι' → M} {g : ι → M} (h : f ∘ e = g) :
     LinearIndependent R g ↔ LinearIndependent R f :=
@@ -1463,7 +1463,7 @@ theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv :
 lean 3 declaration is
   forall (G : Type.{u1}) [_inst_8 : Monoid.{u1} G] (L : Type.{u2}) [_inst_9 : CommRing.{u2} L] [_inst_10 : NoZeroDivisors.{u2} L (Distrib.toHasMul.{u2} L (Ring.toDistrib.{u2} L (CommRing.toRing.{u2} L _inst_9))) (MulZeroClass.toHasZero.{u2} L (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9))))))], LinearIndependent.{max u2 u1, u2, max u1 u2} (MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) => coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) (fun (_x : MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) => G -> L) (MonoidHom.hasCoeToFun.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) f) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9)) (Pi.addCommMonoid.{u1, u2} G (fun (ᾰ : G) => L) (fun (i : G) => AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) (Pi.Function.module.{u1, u2, u2} G L L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9)) (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9))))) (Semiring.toModule.{u2} L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9))))
 but is expected to have type
-  forall (G : Type.{u2}) [_inst_8 : Monoid.{u2} G] (L : Type.{u1}) [_inst_9 : CommRing.{u1} L] [_inst_10 : NoZeroDivisors.{u1} L (NonUnitalNonAssocRing.toMul.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))) (CommMonoidWithZero.toZero.{u1} L (CommSemiring.toCommMonoidWithZero.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))], LinearIndependent.{max u2 u1, u1, max u2 u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => L) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) G L (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G _inst_8)) (MulOneClass.toMul.{u1} L (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9))))) (MonoidHom.monoidHomClass.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))))) f) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)) (Pi.addCommMonoid.{u2, u1} G (fun (ᾰ : G) => L) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (Pi.module.{u2, u1, u1} G (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.14887 : G) => L) L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (fun (i : G) => Semiring.toModule.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9))))
+  forall (G : Type.{u2}) [_inst_8 : Monoid.{u2} G] (L : Type.{u1}) [_inst_9 : CommRing.{u1} L] [_inst_10 : NoZeroDivisors.{u1} L (NonUnitalNonAssocRing.toMul.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))) (CommMonoidWithZero.toZero.{u1} L (CommSemiring.toCommMonoidWithZero.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))], LinearIndependent.{max u2 u1, u1, max u2 u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => L) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) G L (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G _inst_8)) (MulOneClass.toMul.{u1} L (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9))))) (MonoidHom.monoidHomClass.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))))) f) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)) (Pi.addCommMonoid.{u2, u1} G (fun (ᾰ : G) => L) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (Pi.module.{u2, u1, u1} G (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.14887 : G) => L) L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (fun (i : G) => Semiring.toModule.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_monoid_hom linearIndependent_monoidHomₓ'. -/
 -- See, for example, Keith Conrad's note
 --  <https://kconrad.math.uconn.edu/blurbs/galoistheory/linearchar.pdf>

bump to nightly-2023-05-18-03

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

b46e9d53

Diff

@@ -116,7 +116,7 @@ variable {R} {v}
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2], Iff (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), (Eq.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u3, u2} ι M R _inst_1 _inst_2 _inst_5 v) l) (OfNat.ofNat.{u3} M 0 (OfNat.mk.{u3} M 0 (Zero.zero.{u3} M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2))))))) -> (Eq.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) l (OfNat.ofNat.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) 0 (OfNat.mk.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) 0 (Zero.zero.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Finsupp.zero.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.zero.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.zero.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_iff linearIndependent_iffₓ'. -/
 theorem linearIndependent_iff : LinearIndependent R v ↔ ∀ l, Finsupp.total ι M R v l = 0 → l = 0 :=
   by simp [LinearIndependent, LinearMap.ker_eq_bot']
@@ -207,7 +207,7 @@ theorem Fintype.linearIndependent_iff [Fintype ι] :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] [_inst_8 : Fintype.{u1} ι], Iff (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5) (Eq.{succ (max u1 u2)} (Submodule.{u2, max u1 u2} R (forall (i : ι), (fun (i : ι) => R) i) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i))) (LinearMap.ker.{u2, u2, max u1 u2, u3, max (max u1 u2) u3} R R (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) 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_inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.module.{u2, u2, 0, u2, u3} R R Nat ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.module.{u2, u2, 0, max u1 u2, u3} R R Nat (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) => (forall (i : ι), LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) -> (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (forall (i : ι), (fun (i : ι) => R) i) M (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5)) (LinearEquiv.hasCoeToFun.{0, 0, max u1 u2 u3, max (max u1 u2) u3} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (forall (i : ι), (fun (i : ι) => R) i) M (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, max u2 u3} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u1 u2, u3} R R (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u1, max u2 u3, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.module.{u2, u2, 0, u2, u3} R R Nat ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.module.{u2, u2, 0, max u1 u2, u3} R R Nat (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)) (LinearMap.lsum.{u2, u3, u1, u2, 0} R M ι _inst_1 (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) Nat _inst_2 _inst_5 _inst_8 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u1} ι a b)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5))) (fun (i : ι) => LinearMap.smulRight.{u2, u2, u3, u2} R ((fun (i : ι) => R) i) M ((fun (i : ι) => R) i) _inst_1 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) _inst_5 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_1 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (IsScalarTower.left.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2))) (Module.toMulActionWithZero.{u2, u3} R M _inst_1 _inst_2 _inst_5))) (LinearMap.id.{u2, u2} R ((fun (i : ι) => R) i) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) (v i)))) (Bot.bot.{max u1 u2} (Submodule.{u2, max u1 u2} R (forall (i : ι), (fun (i : ι) => R) i) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i))) (Submodule.hasBot.{u2, max u1 u2} R (forall (i : ι), (fun (i : ι) => R) i) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] [_inst_8 : Fintype.{u3} ι], Iff (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) (Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.ker.{u2, u2, max u3 u2, u1, max (max u3 u2) u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun 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(Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) 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(x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u1, 0, max (max u2 u3) u1, max (max u2 u3) u1} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (SemilinearMapClass.distribMulActionHomClass.{0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (LinearMap.lsum.{u2, u1, u3, u2, 0} R M ι _inst_1 (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) Nat _inst_2 _inst_5 _inst_8 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u3} ι a b)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (fun (i : ι) => LinearMap.smulRight.{u2, u2, u1, u2} R R M R _inst_1 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) _inst_5 (Semiring.toModule.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R _inst_1) _inst_5 (IsScalarTower.left.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (LinearMap.id.{u2, u2} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (v i)))) (Bot.bot.{max u3 u2} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (Submodule.instBotSubmodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] [_inst_8 : Fintype.{u3} ι], Iff (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) (Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.ker.{u2, u2, max u3 u2, u1, max (max u3 u2) u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun 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_inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun 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(Semiring.toModule.{u2} R _inst_1)) (v i))) (LinearMap.semilinearMapClass.{u2, u2, max u3 u2, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (max (succ u2) (succ u3)) (succ u1), max (max (succ u2) (succ u3)) (succ u1)} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) 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(x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (_x : forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) _x) (SMulHomClass.toFunLike.{max (max u2 u3) u1, 0, max (max u2 u3) u1, max (max u2 u3) u1} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u1, 0, max (max u2 u3) u1, max (max u2 u3) u1} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (SemilinearMapClass.distribMulActionHomClass.{0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (LinearMap.lsum.{u2, u1, u3, u2, 0} R M ι _inst_1 (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) Nat _inst_2 _inst_5 _inst_8 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u3} ι a b)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (fun (i : ι) => LinearMap.smulRight.{u2, u2, u1, u2} R R M R _inst_1 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) _inst_5 (Semiring.toModule.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R _inst_1) _inst_5 (IsScalarTower.left.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (LinearMap.id.{u2, u2} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (v i)))) (Bot.bot.{max u3 u2} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (Submodule.instBotSubmodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align fintype.linear_independent_iff' Fintype.linearIndependent_iff'ₓ'. -/
 /-- A finite family of vectors `v i` is linear independent iff the linear map that sends
 `c : ι → R` to `∑ i, c i • v i` has the trivial kernel. -/
@@ -289,7 +289,7 @@ theorem LinearIndependent.coe_range (i : LinearIndependent R v) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {M' : Type.{u4}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u4} M'] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] [_inst_6 : Module.{u2, u4} R M' _inst_1 _inst_3], (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5) -> (forall {f : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6}, (Disjoint.{u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (SetLike.partialOrder.{u3, u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u2, u3} R M _inst_1 _inst_2 _inst_5)) (Submodule.orderBot.{u2, u3} R M _inst_1 _inst_2 _inst_5) (Submodule.span.{u2, u3} R M _inst_1 _inst_2 _inst_5 (Set.range.{u3, succ u1} M ι v)) (LinearMap.ker.{u2, u2, u3, u4, max u3 u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)) -> (LinearIndependent.{u1, u2, u4} ι R M' (Function.comp.{succ u1, succ u3, succ u4} ι M M' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
 but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3], (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5) -> (forall {f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6}, (Disjoint.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.completeLattice.{u3, u2} R M _inst_1 _inst_2 _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.span.{u3, u2} R M _inst_1 _inst_2 _inst_5 (Set.range.{u2, succ u4} M ι v)) (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
+  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3], (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5) -> (forall {f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6}, (Disjoint.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.completeLattice.{u3, u2} R M _inst_1 _inst_2 _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.span.{u3, u2} R M _inst_1 _inst_2 _inst_5 (Set.range.{u2, succ u4} M ι v)) (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
 Case conversion may be inaccurate. Consider using '#align linear_independent.map LinearIndependent.mapₓ'. -/
 /-- If `v` is a linearly independent family of vectors and the kernel of a linear map `f` is
 disjoint with the submodule spanned by the vectors of `v`, then `f ∘ v` is a linearly independent
@@ -312,7 +312,7 @@ theorem LinearIndependent.map (hv : LinearIndependent R v) {f : M →ₗ[R] M'}
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {M' : Type.{u4}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u4} M'] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] [_inst_6 : Module.{u2, u4} R M' _inst_1 _inst_3], (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5) -> (forall (f : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (Eq.{succ u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (LinearMap.ker.{u2, u2, u3, u4, max u3 u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (Bot.bot.{u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (Submodule.hasBot.{u2, u3} R M _inst_1 _inst_2 _inst_5))) -> (LinearIndependent.{u1, u2, u4} ι R M' (Function.comp.{succ u1, succ u3, succ u4} ι M M' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
 but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3], (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5) -> (forall (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) (Bot.bot.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.instBotSubmodule.{u3, u2} R M _inst_1 _inst_2 _inst_5))) -> (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
+  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3], (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5) -> (forall (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) (Bot.bot.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.instBotSubmodule.{u3, u2} R M _inst_1 _inst_2 _inst_5))) -> (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
 Case conversion may be inaccurate. Consider using '#align linear_independent.map' LinearIndependent.map'ₓ'. -/
 /-- An injective linear map sends linearly independent families of vectors to linearly independent
 families of vectors. See also `linear_independent.map` for a more general statement. -/
@@ -325,7 +325,7 @@ theorem LinearIndependent.map' (hv : LinearIndependent R v) (f : M →ₗ[R] M')
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {M' : Type.{u4}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u4} M'] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] [_inst_6 : Module.{u2, u4} R M' _inst_1 _inst_3] (f : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (LinearIndependent.{u1, u2, u4} ι R M' (Function.comp.{succ u1, succ u3, succ u4} ι M M' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6) -> (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5)
 but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6) -> (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5)
+  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6) -> (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent.of_comp LinearIndependent.of_compₓ'. -/
 /-- If the image of a family of vectors under a linear map is linearly independent, then so is
 the original family. -/
@@ -341,7 +341,7 @@ theorem LinearIndependent.of_comp (f : M →ₗ[R] M') (hfv : LinearIndependent
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {M' : Type.{u4}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u4} M'] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] [_inst_6 : Module.{u2, u4} R M' _inst_1 _inst_3] (f : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (Eq.{succ u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (LinearMap.ker.{u2, u2, u3, u4, max u3 u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (Bot.bot.{u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (Submodule.hasBot.{u2, u3} R M _inst_1 _inst_2 _inst_5))) -> (Iff (LinearIndependent.{u1, u2, u4} ι R M' (Function.comp.{succ u1, succ u3, succ u4} ι M M' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6) (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5))
 but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) (Bot.bot.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.instBotSubmodule.{u3, u2} R M _inst_1 _inst_2 _inst_5))) -> (Iff (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6) (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5))
+  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) (Bot.bot.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.instBotSubmodule.{u3, u2} R M _inst_1 _inst_2 _inst_5))) -> (Iff (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6) (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5))
 Case conversion may be inaccurate. Consider using '#align linear_map.linear_independent_iff LinearMap.linearIndependent_iffₓ'. -/
 /-- If `f` is an injective linear map, then the family `f ∘ v` is linearly independent
 if and only if the family `v` is linearly independent. -/
@@ -507,7 +507,7 @@ section Subtype
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] {s : Set.{u1} ι}, Iff (LinearIndependent.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) R M (Function.comp.{succ u1, succ u1, succ u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι M v ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeSubtype.{succ u1} ι (fun (x : ι) => Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) x s))))))) _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), (Membership.Mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Submodule.setLike.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) l (Finsupp.supported.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s)) -> (Eq.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u3, u2} ι M R _inst_1 _inst_2 _inst_5 v) l) (OfNat.ofNat.{u3} M 0 (OfNat.mk.{u3} M 0 (Zero.zero.{u3} M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2))))))) -> (Eq.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) l (OfNat.ofNat.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) 0 (OfNat.mk.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) 0 (Zero.zero.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Finsupp.zero.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))))
 but is expected to have type
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_inst_1))) => M) l) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) l (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R 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+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, Iff (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))), (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) l (Finsupp.supported.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R 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_inst_1))) => M) l) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) l (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (Finsupp.zero.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_comp_subtype linearIndependent_comp_subtypeₓ'. -/
 theorem linearIndependent_comp_subtype {s : Set ι} :
     LinearIndependent R (v ∘ coe : s → M) ↔
@@ -532,7 +532,7 @@ theorem linearIndependent_comp_subtype {s : Set ι} :
 lean 3 declaration is
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 but is expected to have type
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(Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v) f) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) _inst_2))))) (Ne.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) f (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.zero.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, Iff (Not (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5)) (Exists.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (f : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => And (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (Submodule.setLike.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) f (Finsupp.supported.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s)) (And (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v) f) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) _inst_2))))) (Ne.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) f (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.zero.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))))))
 Case conversion may be inaccurate. Consider using '#align linear_dependent_comp_subtype' linearDependent_comp_subtype'ₓ'. -/
 theorem linearDependent_comp_subtype' {s : Set ι} :
     ¬LinearIndependent R (v ∘ coe : s → M) ↔
@@ -557,7 +557,7 @@ theorem linearDependent_comp_subtype {s : Set ι} :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x s))))) x) _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))), (Membership.Mem.{max u2 u1, max u2 u1} (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Submodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R 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_inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) (Submodule.setLike.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) -> (Eq.{succ u2} M (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) (fun (_x : LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) => (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u2} R R (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_2 _inst_5 (id.{succ u2} M)) l) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))))) -> (Eq.{max (succ u2) (succ u1)} (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) l (OfNat.ofNat.{max u2 u1} (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) 0 (OfNat.mk.{max u2 u1} (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) 0 (Zero.zero.{max u2 u1} (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Finsupp.zero.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))))
 but is expected to have type
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.setLike.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_2 _inst_5 (id.{succ u2} M)) l) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u1) (succ u2)} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) l (OfNat.ofNat.{max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) 0 (Zero.toOfNat0.{max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R 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+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M s) R M (fun (x : Set.Elem.{u2} M s) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) x) _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))), (Membership.mem.{max u1 u2, max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.setLike.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R 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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u1) (succ u2)} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) l (OfNat.ofNat.{max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) 0 (Zero.toOfNat0.{max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Finsupp.zero.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_subtype linearIndependent_subtypeₓ'. -/
 theorem linearIndependent_subtype {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
@@ -569,7 +569,7 @@ theorem linearIndependent_subtype {s : Set M} :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] {s : Set.{u1} ι}, Iff (LinearIndependent.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) R M (Function.comp.{succ u1, succ u1, succ u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι M v ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeSubtype.{succ u1} ι (fun (x : ι) => Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) x s))))))) _inst_1 _inst_2 _inst_5) (Disjoint.{max u1 u2} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Submodule.setLike.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) (Submodule.orderBot.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.supported.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s) (LinearMap.ker.{u2, u2, max u1 u2, u3, max (max u1 u2) u3} R R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5) (LinearMap.semilinearMapClass.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u3, u2} ι M R _inst_1 _inst_2 _inst_5 v)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, Iff (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5) (Disjoint.{max u2 u3} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Submodule.completeLattice.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.supported.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s) (LinearMap.ker.{u2, u2, max u3 u2, u1, max (max u3 u2) u1} R R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v)))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, Iff (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5) (Disjoint.{max u2 u3} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Submodule.completeLattice.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.supported.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s) (LinearMap.ker.{u2, u2, max u3 u2, u1, max (max u3 u2) u1} R R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5) (LinearMap.semilinearMapClass.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v)))
 Case conversion may be inaccurate. Consider using '#align linear_independent_comp_subtype_disjoint linearIndependent_comp_subtype_disjointₓ'. -/
 theorem linearIndependent_comp_subtype_disjoint {s : Set ι} :
     LinearIndependent R (v ∘ coe : s → M) ↔
@@ -581,7 +581,7 @@ theorem linearIndependent_comp_subtype_disjoint {s : Set ι} :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x s))))) x) _inst_1 _inst_2 _inst_5) (Disjoint.{max u2 u1} (Submodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.partialOrder.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) (Submodule.setLike.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) (Submodule.orderBot.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s) (LinearMap.ker.{u1, u1, max u2 u1, u2, max u2 u1} R R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, u2} R R (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_2 _inst_5 (id.{succ u2} M))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M s) R M (fun (x : Set.Elem.{u2} M s) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) x) _inst_1 _inst_2 _inst_5) (Disjoint.{max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Submodule.completeLattice.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s) (LinearMap.ker.{u1, u1, max u1 u2, u2, max u1 u2} R R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_2 _inst_5 (id.{succ u2} M))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M s) R M (fun (x : Set.Elem.{u2} M s) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) x) _inst_1 _inst_2 _inst_5) (Disjoint.{max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Submodule.completeLattice.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s) (LinearMap.ker.{u1, u1, max u1 u2, u2, max u1 u2} R R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_2 _inst_5 (id.{succ u2} M))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_subtype_disjoint linearIndependent_subtype_disjointₓ'. -/
 theorem linearIndependent_subtype_disjoint {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
@@ -593,7 +593,7 @@ theorem linearIndependent_subtype_disjoint {s : Set M} :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x s))))) x) _inst_1 _inst_2 _inst_5) (Eq.{succ (max u2 u1)} (Submodule.{u1, max u2 u1} R (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) (Submodule.setLike.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) _inst_1 (Submodule.addCommMonoid.{u1, max u2 u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) _inst_1 (Submodule.addCommMonoid.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.module.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M s) R M (fun (x : Set.Elem.{u2} M s) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) x) _inst_1 _inst_2 _inst_5) (Eq.{max (succ u1) (succ u2)} (Submodule.{u1, max u1 u2} R (Subtype.{succ (max u2 u1)} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (x : Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => Membership.mem.{max u2 u1, 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+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M s) R M (fun (x : Set.Elem.{u2} M s) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) x) _inst_1 _inst_2 _inst_5) (Eq.{max (succ u1) (succ u2)} (Submodule.{u1, max u1 u2} R (Subtype.{succ (max u2 u1)} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (x : Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => Membership.mem.{max u2 u1, max u2 u1} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u1, max 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R _inst_1)))) x (Finsupp.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_5)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_5 (Set.image.{u2, u2} M M (id.{succ u2} M) s)))) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R 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_inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_5 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_5 (Set.image.{u2, u2} M M (id.{succ u2} M) s))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) 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Membership.mem.{max u2 u1, max u2 u1} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.setLike.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) x (Finsupp.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))) _inst_1 (Submodule.addCommMonoid.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.module.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_iff_total_on linearIndependent_iff_totalOnₓ'. -/
 theorem linearIndependent_iff_totalOn {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔ (Finsupp.totalOn M M R id s).ker = ⊥ := by
@@ -699,7 +699,7 @@ variable {a b : R} {x y : M}
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], Iff (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Function.Injective.{max (succ u1) (succ u2), succ u3} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u1, u3, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 v)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], Iff (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Function.Injective.{max (succ u3) (succ u2), succ u1} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v)))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], Iff (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Function.Injective.{max (succ u3) (succ u2), succ u1} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v)))
 Case conversion may be inaccurate. Consider using '#align linear_independent_iff_injective_total linearIndependent_iff_injective_totalₓ'. -/
 theorem linearIndependent_iff_injective_total :
     LinearIndependent R v ↔ Function.Injective (Finsupp.total ι M R v) :=
@@ -711,7 +711,7 @@ theorem linearIndependent_iff_injective_total :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (Function.Injective.{max (succ u1) (succ u2), succ u3} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u1, u3, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 v)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (Function.Injective.{max (succ u3) (succ u2), succ u1} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v)))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (Function.Injective.{max (succ u3) (succ u2), succ u1} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v)))
 Case conversion may be inaccurate. Consider using '#align linear_independent.injective_total LinearIndependent.injective_totalₓ'. -/
 alias linearIndependent_iff_injective_total ↔ LinearIndependent.injective_total _
 #align linear_independent.injective_total LinearIndependent.injective_total
@@ -944,7 +944,7 @@ theorem LinearIndependent.not_mem_span_image [Nontrivial R] (hv : LinearIndepend
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_8 : Nontrivial.{u2} R], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall {x : ι} (f : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))), (Not (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) x (Finsupp.support.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) f))) -> (Ne.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u1, u3, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 v) f) (v x)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Nontrivial.{u2} R], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall {x : ι} (f : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))), (Not (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) x (Finsupp.support.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) f))) -> (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) f) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v) f) (v x)))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Nontrivial.{u2} R], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall {x : ι} (f : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))), (Not (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) x (Finsupp.support.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) f))) -> (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) f) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v) f) (v x)))
 Case conversion may be inaccurate. Consider using '#align linear_independent.total_ne_of_not_mem_support LinearIndependent.total_ne_of_not_mem_supportₓ'. -/
 theorem LinearIndependent.total_ne_of_not_mem_support [Nontrivial R] (hv : LinearIndependent R v)
     {x : ι} (f : ι →₀ R) (h : x ∉ f.support) : Finsupp.total ι M R v f ≠ v x :=
@@ -1135,7 +1135,7 @@ def LinearIndependent.repr (hv : LinearIndependent R v) : span R (range v) →
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))), Eq.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ 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(Ring.toSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align linear_independent.total_repr LinearIndependent.total_reprₓ'. -/
 @[simp]
 theorem LinearIndependent.total_repr (x) : Finsupp.total ι M R v (hv.repr x) = x :=
@@ -1157,7 +1157,7 @@ theorem LinearIndependent.total_comp_repr :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5), Eq.{succ u3} (Submodule.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (LinearMap.ker.{u2, u2, u3, max u1 u2, max u3 u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.semilinearMapClass.{u2, u2, u3, max u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Bot.bot.{u3} (Submodule.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Submodule.hasBot.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5), Eq.{succ u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (LinearMap.ker.{u1, u1, u2, max u3 u1, max (max u3 u1) u2} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, max u1 u3} 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))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Bot.bot.{u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Submodule.instBotSubmodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))))
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5), Eq.{succ u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (LinearMap.ker.{u1, u1, u2, max u3 u1, max (max u3 u1) u2} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, max u1 u3} 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))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.semilinearMapClass.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Bot.bot.{u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Submodule.instBotSubmodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_ker LinearIndependent.repr_kerₓ'. -/
 theorem LinearIndependent.repr_ker : hv.repr.ker = ⊥ := by
   rw [LinearIndependent.repr, LinearEquiv.ker]
@@ -1167,7 +1167,7 @@ theorem LinearIndependent.repr_ker : hv.repr.ker = ⊥ := by
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5), Eq.{succ (max u1 u2)} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.range.{u2, u2, u3, max u1 u2, max u3 u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.semilinearMapClass.{u2, u2, u3, max u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Top.top.{max u1 u2} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.hasTop.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5), Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.range.{u2, u2, u1, max u3 u2, max (max u3 u2) u1} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, max u2 u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Top.top.{max u3 u2} (Submodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.instTopSubmodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5), Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.range.{u2, u2, u1, max u3 u2, max (max u3 u2) u1} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) 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(Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, max u2 u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} 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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.semilinearMapClass.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Top.top.{max u3 u2} (Submodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.instTopSubmodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_range LinearIndependent.repr_rangeₓ'. -/
 theorem LinearIndependent.repr_range : hv.repr.range = ⊤ := by
   rw [LinearIndependent.repr, LinearEquiv.range]
@@ -1177,7 +1177,7 @@ theorem LinearIndependent.repr_range : hv.repr.range = ⊤ := by
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) {l : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))} {x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq LinearIndependent.repr_eqₓ'. -/
 theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M R v l = ↑x) :
     hv.repr x = l :=
@@ -1199,7 +1199,7 @@ theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (i : ι) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))), (Eq.{succ u3} M ((fun (a : Type.{u3}) (b : 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(Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) 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(AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1)))))))))
 but is expected to have type
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(Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv) x) (Finsupp.single.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) i (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (i : ι) (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))), (Eq.{succ u2} M 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x 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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv) x) (Finsupp.single.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) i (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq_single LinearIndependent.repr_eq_singleₓ'. -/
 theorem LinearIndependent.repr_eq_single (i) (x) (hx : ↑x = v i) : hv.repr x = Finsupp.single i 1 :=
   by
@@ -1211,7 +1211,7 @@ theorem LinearIndependent.repr_eq_single (i) (x) (hx : ↑x = v i) : hv.repr x =
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) [_inst_8 : Nontrivial.{u2} R] (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))), Eq.{max (succ u3) 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(NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv) x))
 but is expected to have type
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(fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) [_inst_8 : Nontrivial.{u2} R] (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι 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(fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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 Case conversion may be inaccurate. Consider using '#align linear_independent.span_repr_eq LinearIndependent.span_repr_eqₓ'. -/
 theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
     Span.repr R (Set.range v) x = (hv.repr x).equivMapDomain (Equiv.ofInjective _ hv.Injective) :=
@@ -1418,7 +1418,7 @@ open LinearMap
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {M' : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3)] {s : Set.{u2} M} {f : LinearMap.{u1, u1, u2, u3} 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))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6}, (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => 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(Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) s)) M' (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M') Type.{u3} (Set.hasCoeToSort.{u3} M') (Set.image.{u2, u3} M M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} 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))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} 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))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) 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(AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) s)))))) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_6)
 but is expected to have type
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(Disjoint.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 s) (LinearMap.ker.{u2, u2, u3, u1, max u3 u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (LinearIndependent.{u1, u2, u1} (Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) R M' (fun (x : Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) => Subtype.val.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Set.{u1} M') (Set.instMembershipSet.{u1} M') x (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') a) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_6)
+  forall {R : Type.{u2}} {M : Type.{u3}} {M' : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_6 : Module.{u2, u1} R M' (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)] {s : Set.{u3} M} {f : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6}, (LinearIndependent.{u3, u2, u3} (Set.Elem.{u3} M s) R M (fun (x : Set.Elem.{u3} M s) => Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x s) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (Disjoint.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 s) (LinearMap.ker.{u2, u2, u3, u1, max u3 u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (LinearIndependent.{u1, u2, u1} (Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) R M' (fun (x : Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) => Subtype.val.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Set.{u1} M') (Set.instMembershipSet.{u1} M') x (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') a) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_6)
 Case conversion may be inaccurate. Consider using '#align linear_independent.image_subtype LinearIndependent.image_subtypeₓ'. -/
 theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
     (hs : LinearIndependent R (fun x => x : s → M)) (hf_inj : Disjoint (span R s) f.ker) :
@@ -1433,7 +1433,7 @@ theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
 lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u2} M' _inst_3)) _inst_6 (Prod.module.{u1, u3, u2} R M M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.inr.{u1, u3, u2} R M M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_3) _inst_5 _inst_6)) t))) x) (Ring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u3, u2} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_3)) (Prod.module.{u1, u3, u2} R M M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_3) _inst_5 _inst_6))
 Case conversion may be inaccurate. Consider using '#align linear_independent.inl_union_inr LinearIndependent.inl_union_inrₓ'. -/
 theorem LinearIndependent.inl_union_inr {s : Set M} {t : Set M'}
     (hs : LinearIndependent R (fun x => x : s → M))
@@ -1449,7 +1449,7 @@ theorem LinearIndependent.inl_union_inr {s : Set M} {t : Set M'}
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u4}} {M' : Type.{u5}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u4} M] [_inst_3 : AddCommGroup.{u5} M'] [_inst_5 : Module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] [_inst_6 : Module.{u3, u5} R M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)] {v : ι -> M} {v' : ι' -> M'}, (LinearIndependent.{u1, u3, u4} ι R M v (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5) -> (LinearIndependent.{u2, u3, u5} ι' R M' v' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_6) -> (LinearIndependent.{max u1 u2, u3, max u4 u5} (Sum.{u1, u2} ι ι') R (Prod.{u4, u5} M M') (Sum.elim.{u1, u2, succ (max u4 u5)} ι ι' (Prod.{u4, u5} M M') (Function.comp.{succ u1, succ u4, succ (max u4 u5)} ι M (Prod.{u4, u5} M M') (coeFn.{max (succ u4) (succ (max u4 u5)), max (succ u4) (succ (max u4 u5))} (LinearMap.{u3, u3, u4, max u4 u5} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M (Prod.{u4, u5} M M') (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (Prod.addCommMonoid.{u4, u5} M M' (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)) _inst_5 (Prod.module.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6)) (fun (_x : LinearMap.{u3, u3, u4, max u4 u5} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M (Prod.{u4, u5} M M') (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (Prod.addCommMonoid.{u4, u5} M M' (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)) _inst_5 (Prod.module.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6)) => M -> (Prod.{u4, u5} M M')) (LinearMap.hasCoeToFun.{u3, u3, u4, max u4 u5} R R M (Prod.{u4, u5} M M') (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (Prod.addCommMonoid.{u4, u5} M M' (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)) _inst_5 (Prod.module.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (LinearMap.inl.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6)) v) (Function.comp.{succ 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(Prod.addCommMonoid.{u4, u5} M M' (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)) _inst_6 (Prod.module.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6)) => M' -> (Prod.{u4, u5} M M')) (LinearMap.hasCoeToFun.{u3, u3, u5, max u4 u5} R R M' (Prod.{u4, u5} M M') (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) (Prod.addCommMonoid.{u4, u5} M M' (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)) _inst_6 (Prod.module.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (LinearMap.inr.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6)) v')) (Ring.toSemiring.{u3} R _inst_1) (Prod.addCommMonoid.{u4, u5} M M' (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)) (Prod.module.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6))
 but is expected to have type
-  forall {ι : Type.{u5}} {ι' : Type.{u2}} {R : Type.{u4}} {M : Type.{u3}} {M' : Type.{u1}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_6 : Module.{u4, u1} R M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)] {v : ι -> M} {v' : ι' -> M'}, (LinearIndependent.{u5, u4, u3} ι R M v (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearIndependent.{u2, u4, u1} ι' R M' v' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_6) -> (LinearIndependent.{max u2 u5, u4, max u3 u1} (Sum.{u5, u2} ι ι') R (Prod.{u3, u1} M M') (Sum.elim.{u5, u2, succ (max u3 u1)} ι ι' (Prod.{u3, u1} M M') (Function.comp.{succ u5, succ u3, succ (max u3 u1)} ι M (Prod.{u3, u1} M M') (FunLike.coe.{max (succ u3) (succ u1), succ u3, max (succ u3) (succ u1)} (LinearMap.{u4, u4, u3, max u1 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))) M (Prod.{u3, u1} M M') (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_5 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Prod.{u3, u1} M M') _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u3 u1} R R M (Prod.{u3, u1} M M') (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_5 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (LinearMap.inl.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) v) (Function.comp.{succ u2, succ u1, max (succ u3) (succ u1)} ι' M' (Prod.{u3, u1} M M') (FunLike.coe.{max (succ u3) (succ u1), succ u1, max (succ u3) (succ u1)} (LinearMap.{u4, u4, u1, max u1 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))) M' (Prod.{u3, u1} M M') (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_6 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) M' (fun (_x : M') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M') => Prod.{u3, u1} M M') _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, max u3 u1} R R M' (Prod.{u3, u1} M M') (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_6 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (LinearMap.inr.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) v')) (Ring.toSemiring.{u4} R _inst_1) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6))
+  forall {ι : Type.{u5}} {ι' : Type.{u2}} {R : Type.{u4}} {M : Type.{u3}} {M' : Type.{u1}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_6 : Module.{u4, u1} R M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)] {v : ι -> M} {v' : ι' -> M'}, (LinearIndependent.{u5, u4, u3} ι R M v (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearIndependent.{u2, u4, u1} ι' R M' v' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_6) -> (LinearIndependent.{max u2 u5, u4, max u3 u1} (Sum.{u5, u2} ι ι') R (Prod.{u3, u1} M M') (Sum.elim.{u5, u2, succ (max u3 u1)} ι ι' (Prod.{u3, u1} M M') (Function.comp.{succ u5, succ u3, succ (max u3 u1)} ι M (Prod.{u3, u1} M M') (FunLike.coe.{max (succ u3) (succ u1), succ u3, max (succ u3) (succ u1)} (LinearMap.{u4, u4, u3, max u1 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))) M (Prod.{u3, u1} M M') (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_5 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Prod.{u3, u1} M M') _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u3 u1} R R M (Prod.{u3, u1} M M') (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_5 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (LinearMap.inl.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) v) (Function.comp.{succ u2, succ u1, max (succ u3) (succ u1)} ι' M' (Prod.{u3, u1} M M') (FunLike.coe.{max (succ u3) (succ u1), succ u1, max (succ u3) (succ u1)} (LinearMap.{u4, u4, u1, max u1 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))) M' (Prod.{u3, u1} M M') (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_6 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) M' (fun (_x : M') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M') => Prod.{u3, u1} M M') _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, max u3 u1} R R M' (Prod.{u3, u1} M M') (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_6 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (LinearMap.inr.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) v')) (Ring.toSemiring.{u4} R _inst_1) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6))
 Case conversion may be inaccurate. Consider using '#align linear_independent_inl_union_inr' linearIndependent_inl_union_inr'ₓ'. -/
 theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv : LinearIndependent R v)
     (hv' : LinearIndependent R v') :

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -1564,7 +1564,7 @@ theorem linearIndependent_monoidHom (G : Type _) [Monoid G] (L : Type _) [CommRi
 
 /- warning: le_of_span_le_span -> le_of_span_le_span is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Nontrivial.{u1} R] {s : Set.{u2} M} {t : Set.{u2} M} {u : Set.{u2} M}, (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) u) R M ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) u) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) u) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) u) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) u) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x u)))))) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (HasSubset.Subset.{u2} (Set.{u2} M) (Set.hasSubset.{u2} M) s u) -> (HasSubset.Subset.{u2} (Set.{u2} M) (Set.hasSubset.{u2} M) t u) -> (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)))) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 s) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 t)) -> (HasSubset.Subset.{u2} (Set.{u2} M) (Set.hasSubset.{u2} M) s t)
 but is expected to have type
   forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Nontrivial.{u2} R] {s : Set.{u1} M} {t : Set.{u1} M} {u : Set.{u1} M}, (LinearIndependent.{u1, u2, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x u)) R M (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x u)) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (HasSubset.Subset.{u1} (Set.{u1} M) (Set.instHasSubsetSet.{u1} M) s u) -> (HasSubset.Subset.{u1} (Set.{u1} M) (Set.instHasSubsetSet.{u1} M) t u) -> (LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 s) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 t)) -> (HasSubset.Subset.{u1} (Set.{u1} M) (Set.instHasSubsetSet.{u1} M) s t)
 Case conversion may be inaccurate. Consider using '#align le_of_span_le_span le_of_span_le_spanₓ'. -/
@@ -1579,7 +1579,7 @@ theorem le_of_span_le_span [Nontrivial R] {s t u : Set M} (hl : LinearIndependen
 
 /- warning: span_le_span_iff -> span_le_span_iff is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Nontrivial.{u1} R] {s : Set.{u2} M} {t : Set.{u2} M} {u : Set.{u2} M}, (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) u) R M ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) u) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) u) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) u) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) u) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x u)))))) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (HasSubset.Subset.{u2} (Set.{u2} M) (Set.hasSubset.{u2} M) s u) -> (HasSubset.Subset.{u2} (Set.{u2} M) (Set.hasSubset.{u2} M) t u) -> (Iff (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)))) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 s) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 t)) (HasSubset.Subset.{u2} (Set.{u2} M) (Set.hasSubset.{u2} M) s t))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Nontrivial.{u1} R] {s : Set.{u2} M} {t : Set.{u2} M} {u : Set.{u2} M}, (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) u) R M ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) u) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) u) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) u) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) u) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x u)))))) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (HasSubset.Subset.{u2} (Set.{u2} M) (Set.hasSubset.{u2} M) s u) -> (HasSubset.Subset.{u2} (Set.{u2} M) (Set.hasSubset.{u2} M) t u) -> (Iff (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)))) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 s) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 t)) (HasSubset.Subset.{u2} (Set.{u2} M) (Set.hasSubset.{u2} M) s t))
 but is expected to have type
   forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Nontrivial.{u2} R] {s : Set.{u1} M} {t : Set.{u1} M} {u : Set.{u1} M}, (LinearIndependent.{u1, u2, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x u)) R M (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x u)) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (HasSubset.Subset.{u1} (Set.{u1} M) (Set.instHasSubsetSet.{u1} M) s u) -> (HasSubset.Subset.{u1} (Set.{u1} M) (Set.instHasSubsetSet.{u1} M) t u) -> (Iff (LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 s) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 t)) (HasSubset.Subset.{u1} (Set.{u1} M) (Set.instHasSubsetSet.{u1} M) s t))
 Case conversion may be inaccurate. Consider using '#align span_le_span_iff span_le_span_iffₓ'. -/

bump to nightly-2023-05-16-14

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

b356e20f

Diff

@@ -790,7 +790,7 @@ theorem LinearIndependent.image {ι} {s : Set ι} {f : ι → M}
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {G : Type.{u4}} [hG : Group.{u4} G] [_inst_8 : DistribMulAction.{u4, u2} G R (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1))))] [_inst_9 : DistribMulAction.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))] [_inst_10 : IsScalarTower.{u4, u2, u3} G R M (SMulZeroClass.toHasSmul.{u4, u2} G R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1)))))) (DistribSMul.toSmulZeroClass.{u4, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{u4, u2} G R (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1)))) _inst_8))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)))) (SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u4, u2, u3} G R M (SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u1, u2, u3} ι R M (SMul.smul.{max u1 u4, max u1 u3} (ι -> G) (ι -> M) (Pi.smul'.{u1, u4, u3} ι (fun (ᾰ : ι) => G) (fun (ᾰ : ι) => M) (fun (i : ι) => SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9)))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)
 but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {G : Type.{u3}} [hG : Group.{u3} G] [_inst_8 : DistribMulAction.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))] [_inst_9 : DistribMulAction.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))] [_inst_10 : IsScalarTower.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u2} G R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (DistribSMul.toSMulZeroClass.{u3, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))) (DistribMulAction.toDistribSMul.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1))) _inst_8))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u4, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u4, u2, u1} ι R M (HSMul.hSMul.{max u4 u3, max u4 u1, max u4 u1} (ι -> G) (ι -> M) (ι -> M) (instHSMul.{max u4 u3, max u4 u1} (ι -> G) (ι -> M) (Pi.smul'.{u4, u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6785 : ι) => G) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6779 : ι) => M) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
+  forall {ι : Type.{u4}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {G : Type.{u3}} [hG : Group.{u3} G] [_inst_8 : DistribMulAction.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))] [_inst_9 : DistribMulAction.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))] [_inst_10 : IsScalarTower.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u2} G R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (DistribSMul.toSMulZeroClass.{u3, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))) (DistribMulAction.toDistribSMul.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1))) _inst_8))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u4, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u4, u2, u1} ι R M (HSMul.hSMul.{max u4 u3, max u4 u1, max u4 u1} (ι -> G) (ι -> M) (ι -> M) (instHSMul.{max u4 u3, max u4 u1} (ι -> G) (ι -> M) (Pi.smul'.{u4, u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6779 : ι) => G) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6773 : ι) => M) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent.group_smul LinearIndependent.group_smulₓ'. -/
 theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulAction G R]
     [DistribMulAction G M] [IsScalarTower G R M] [SMulCommClass G R M] {v : ι → M}
@@ -811,7 +811,7 @@ theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulActi
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {v : ι -> M}, (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall (w : ι -> (Units.{u2} R (Ring.toMonoid.{u2} R _inst_1))), LinearIndependent.{u1, u2, u3} ι R M (SMul.smul.{max u1 u2, max u1 u3} (ι -> (Units.{u2} R (Ring.toMonoid.{u2} R _inst_1))) (ι -> M) (Pi.smul'.{u1, u2, u3} ι (fun (ᾰ : ι) => Units.{u2} R (Ring.toMonoid.{u2} R _inst_1)) (fun (ᾰ : ι) => M) (fun (i : ι) => Units.hasSmul.{u2, u3} R M (Ring.toMonoid.{u2} R _inst_1) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {v : ι -> M}, (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))), LinearIndependent.{u3, u2, u1} ι R M (HSMul.hSMul.{max u3 u2, max u3 u1, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (ι -> M) (instHSMul.{max u3 u2, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.7015 : ι) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.7009 : ι) => M) (fun (i : ι) => Units.instSMulUnits.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {v : ι -> M}, (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))), LinearIndependent.{u3, u2, u1} ι R M (HSMul.hSMul.{max u3 u2, max u3 u1, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (ι -> M) (instHSMul.{max u3 u2, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.7009 : ι) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.7003 : ι) => M) (fun (i : ι) => Units.instSMulUnits.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent.units_smul LinearIndependent.units_smulₓ'. -/
 -- This lemma cannot be proved with `linear_independent.group_smul` since the action of
 -- `Rˣ` on `R` is not commutative.
@@ -1463,7 +1463,7 @@ theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv :
 lean 3 declaration is
   forall (G : Type.{u1}) [_inst_8 : Monoid.{u1} G] (L : Type.{u2}) [_inst_9 : CommRing.{u2} L] [_inst_10 : NoZeroDivisors.{u2} L (Distrib.toHasMul.{u2} L (Ring.toDistrib.{u2} L (CommRing.toRing.{u2} L _inst_9))) (MulZeroClass.toHasZero.{u2} L (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9))))))], LinearIndependent.{max u2 u1, u2, max u1 u2} (MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) => coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) (fun (_x : MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) => G -> L) (MonoidHom.hasCoeToFun.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) f) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9)) (Pi.addCommMonoid.{u1, u2} G (fun (ᾰ : G) => L) (fun (i : G) => AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) (Pi.Function.module.{u1, u2, u2} G L L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9)) (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9))))) (Semiring.toModule.{u2} L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9))))
 but is expected to have type
-  forall (G : Type.{u2}) [_inst_8 : Monoid.{u2} G] (L : Type.{u1}) [_inst_9 : CommRing.{u1} L] [_inst_10 : NoZeroDivisors.{u1} L (NonUnitalNonAssocRing.toMul.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))) (CommMonoidWithZero.toZero.{u1} L (CommSemiring.toCommMonoidWithZero.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))], LinearIndependent.{max u2 u1, u1, max u2 u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => L) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) G L (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G _inst_8)) (MulOneClass.toMul.{u1} L (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9))))) (MonoidHom.monoidHomClass.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))))) f) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)) (Pi.addCommMonoid.{u2, u1} G (fun (ᾰ : G) => L) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (Pi.module.{u2, u1, u1} G (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.14997 : G) => L) L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (fun (i : G) => Semiring.toModule.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9))))
+  forall (G : Type.{u2}) [_inst_8 : Monoid.{u2} G] (L : Type.{u1}) [_inst_9 : CommRing.{u1} L] [_inst_10 : NoZeroDivisors.{u1} L (NonUnitalNonAssocRing.toMul.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))) (CommMonoidWithZero.toZero.{u1} L (CommSemiring.toCommMonoidWithZero.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))], LinearIndependent.{max u2 u1, u1, max u2 u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => L) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) G L (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G _inst_8)) (MulOneClass.toMul.{u1} L (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9))))) (MonoidHom.monoidHomClass.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))))) f) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)) (Pi.addCommMonoid.{u2, u1} G (fun (ᾰ : G) => L) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (Pi.module.{u2, u1, u1} G (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.14887 : G) => L) L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (fun (i : G) => Semiring.toModule.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_monoid_hom linearIndependent_monoidHomₓ'. -/
 -- See, for example, Keith Conrad's note
 --  <https://kconrad.math.uconn.edu/blurbs/galoistheory/linearchar.pdf>

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -642,8 +642,8 @@ theorem linearIndependent_of_finite (s : Set M)
 #align linear_independent_of_finite linearIndependent_of_finite
 -/
 
-#print linearIndependent_unionᵢ_of_directed /-
-theorem linearIndependent_unionᵢ_of_directed {η : Type _} {s : η → Set M} (hs : Directed (· ⊆ ·) s)
+#print linearIndependent_iUnion_of_directed /-
+theorem linearIndependent_iUnion_of_directed {η : Type _} {s : η → Set M} (hs : Directed (· ⊆ ·) s)
     (h : ∀ i, LinearIndependent R (fun x => x : s i → M)) :
     LinearIndependent R (fun x => x : (⋃ i, s i) → M) :=
   by
@@ -656,26 +656,26 @@ theorem linearIndependent_unionᵢ_of_directed {η : Type _} {s : η → Set M}
   · refine' (linearIndependent_empty _ _).mono _
     rintro _ ⟨_, ⟨i, _⟩, _⟩
     exact hη ⟨i⟩
-#align linear_independent_Union_of_directed linearIndependent_unionᵢ_of_directed
+#align linear_independent_Union_of_directed linearIndependent_iUnion_of_directed
 -/
 
-#print linearIndependent_unionₛ_of_directed /-
-theorem linearIndependent_unionₛ_of_directed {s : Set (Set M)} (hs : DirectedOn (· ⊆ ·) s)
+#print linearIndependent_sUnion_of_directed /-
+theorem linearIndependent_sUnion_of_directed {s : Set (Set M)} (hs : DirectedOn (· ⊆ ·) s)
     (h : ∀ a ∈ s, LinearIndependent R (fun x => x : (a : Set M) → M)) :
     LinearIndependent R (fun x => x : ⋃₀ s → M) := by
   rw [sUnion_eq_Union] <;>
-    exact linearIndependent_unionᵢ_of_directed hs.directed_coe (by simpa using h)
-#align linear_independent_sUnion_of_directed linearIndependent_unionₛ_of_directed
+    exact linearIndependent_iUnion_of_directed hs.directed_coe (by simpa using h)
+#align linear_independent_sUnion_of_directed linearIndependent_sUnion_of_directed
 -/
 
-#print linearIndependent_bunionᵢ_of_directed /-
-theorem linearIndependent_bunionᵢ_of_directed {η} {s : Set η} {t : η → Set M}
+#print linearIndependent_biUnion_of_directed /-
+theorem linearIndependent_biUnion_of_directed {η} {s : Set η} {t : η → Set M}
     (hs : DirectedOn (t ⁻¹'o (· ⊆ ·)) s) (h : ∀ a ∈ s, LinearIndependent R (fun x => x : t a → M)) :
     LinearIndependent R (fun x => x : (⋃ a ∈ s, t a) → M) := by
   rw [bUnion_eq_Union] <;>
     exact
-      linearIndependent_unionᵢ_of_directed (directed_comp.2 <| hs.directed_coe) (by simpa using h)
-#align linear_independent_bUnion_of_directed linearIndependent_bunionᵢ_of_directed
+      linearIndependent_iUnion_of_directed (directed_comp.2 <| hs.directed_coe) (by simpa using h)
+#align linear_independent_bUnion_of_directed linearIndependent_biUnion_of_directed
 -/
 
 end Subtype
@@ -1024,38 +1024,38 @@ theorem LinearIndependent.union {s t : Set M} (hs : LinearIndependent R (fun x =
   (hs.sum_type ht <| by simpa).to_subtype_range' <| by simp
 #align linear_independent.union LinearIndependent.union
 
-/- warning: linear_independent_Union_finite_subtype -> linearIndependent_unionᵢ_finite_subtype is a dubious translation:
+/- warning: linear_independent_Union_finite_subtype -> linearIndependent_iUnion_finite_subtype is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} {f : ι -> (Set.{u2} M)}, (forall (i : ι), LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (f i)) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (f i)) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (f i)) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (f i)) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (f i)) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (f i)) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x (f i)))))) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (forall (i : ι) (t : Set.{u3} ι), (Set.Finite.{u3} ι t) -> (Not (Membership.Mem.{u3, u3} ι (Set.{u3} ι) (Set.hasMem.{u3} ι) i t)) -> (Disjoint.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) (Submodule.orderBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (f i)) (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) ι (fun (i : ι) => supᵢ.{u2, 0} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) (Membership.Mem.{u3, u3} ι (Set.{u3} ι) (Set.hasMem.{u3} ι) i t) (fun (H : Membership.Mem.{u3, u3} ι (Set.{u3} ι) (Set.hasMem.{u3} ι) i t) => Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (f i)))))) -> (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))))))) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} {f : ι -> (Set.{u2} M)}, (forall (i : ι), LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (f i)) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (f i)) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (f i)) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (f i)) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (f i)) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (f i)) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x (f i)))))) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (forall (i : ι) (t : Set.{u3} ι), (Set.Finite.{u3} ι t) -> (Not (Membership.Mem.{u3, u3} ι (Set.{u3} ι) (Set.hasMem.{u3} ι) i t)) -> (Disjoint.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) (Submodule.orderBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (f i)) (iSup.{u2, succ u3} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) ι (fun (i : ι) => iSup.{u2, 0} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) (Membership.Mem.{u3, u3} ι (Set.{u3} ι) (Set.hasMem.{u3} ι) i t) (fun (H : Membership.Mem.{u3, u3} ι (Set.{u3} ι) (Set.hasMem.{u3} ι) i t) => Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (f i)))))) -> (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.iUnion.{u2, succ u3} M ι (fun (i : ι) => f i))) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.iUnion.{u2, succ u3} M ι (fun (i : ι) => f i))) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.iUnion.{u2, succ u3} M ι (fun (i : ι) => f i))) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.iUnion.{u2, succ u3} M ι (fun (i : ι) => f i))) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.iUnion.{u2, succ u3} M ι (fun (i : ι) => f i))) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.iUnion.{u2, succ u3} M ι (fun (i : ι) => f i))) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x (Set.iUnion.{u2, succ u3} M ι (fun (i : ι) => f i))))))) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} {f : ι -> (Set.{u2} M)}, (forall (i : ι), LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M (f i)) R M (fun (x : Set.Elem.{u2} M (f i)) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (f i)) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (forall (i : ι) (t : Set.{u3} ι), (Set.Finite.{u3} ι t) -> (Not (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i t)) -> (Disjoint.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (f i)) (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) ι (fun (i : ι) => supᵢ.{u2, 0} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i t) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i t) => Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (f i)))))) -> (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) R M (fun (x : Set.Elem.{u2} M (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)
-Case conversion may be inaccurate. Consider using '#align linear_independent_Union_finite_subtype linearIndependent_unionᵢ_finite_subtypeₓ'. -/
-theorem linearIndependent_unionᵢ_finite_subtype {ι : Type _} {f : ι → Set M}
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} {f : ι -> (Set.{u2} M)}, (forall (i : ι), LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M (f i)) R M (fun (x : Set.Elem.{u2} M (f i)) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (f i)) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (forall (i : ι) (t : Set.{u3} ι), (Set.Finite.{u3} ι t) -> (Not (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i t)) -> (Disjoint.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (f i)) (iSup.{u2, succ u3} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) ι (fun (i : ι) => iSup.{u2, 0} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i t) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i t) => Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (f i)))))) -> (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M (Set.iUnion.{u2, succ u3} M ι (fun (i : ι) => f i))) R M (fun (x : Set.Elem.{u2} M (Set.iUnion.{u2, succ u3} M ι (fun (i : ι) => f i))) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (Set.iUnion.{u2, succ u3} M ι (fun (i : ι) => f i))) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)
+Case conversion may be inaccurate. Consider using '#align linear_independent_Union_finite_subtype linearIndependent_iUnion_finite_subtypeₓ'. -/
+theorem linearIndependent_iUnion_finite_subtype {ι : Type _} {f : ι → Set M}
     (hl : ∀ i, LinearIndependent R (fun x => x : f i → M))
     (hd : ∀ i, ∀ t : Set ι, t.Finite → i ∉ t → Disjoint (span R (f i)) (⨆ i ∈ t, span R (f i))) :
     LinearIndependent R (fun x => x : (⋃ i, f i) → M) :=
   by
   rw [Union_eq_Union_finset f]
-  apply linearIndependent_unionᵢ_of_directed
+  apply linearIndependent_iUnion_of_directed
   · apply directed_of_sup
     exact fun t₁ t₂ ht => Union_mono fun i => Union_subset_Union_const fun h => ht h
   intro t
   induction' t using Finset.induction_on with i s his ih
   · refine' (linearIndependent_empty _ _).mono _
     simp
-  · rw [Finset.set_bunionᵢ_insert]
+  · rw [Finset.set_biUnion_insert]
     refine' (hl _).union ih _
     rw [span_Union₂]
     exact hd i s s.finite_to_set his
-#align linear_independent_Union_finite_subtype linearIndependent_unionᵢ_finite_subtype
+#align linear_independent_Union_finite_subtype linearIndependent_iUnion_finite_subtype
 
-/- warning: linear_independent_Union_finite -> linearIndependent_unionᵢ_finite is a dubious translation:
+/- warning: linear_independent_Union_finite -> linearIndependent_iUnion_finite is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {η : Type.{u3}} {ιs : η -> Type.{u4}} {f : forall (j : η), (ιs j) -> M}, (forall (j : η), LinearIndependent.{u4, u1, u2} (ιs j) R M (f j) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (forall (i : η) (t : Set.{u3} η), (Set.Finite.{u3} η t) -> (Not (Membership.Mem.{u3, u3} η (Set.{u3} η) (Set.hasMem.{u3} η) i t)) -> (Disjoint.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) (Submodule.orderBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u4} M (ιs i) (f i))) (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) η (fun (i : η) => supᵢ.{u2, 0} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) (Membership.Mem.{u3, u3} η (Set.{u3} η) (Set.hasMem.{u3} η) i t) (fun (H : Membership.Mem.{u3, u3} η (Set.{u3} η) (Set.hasMem.{u3} η) i t) => Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u4} M (ιs i) (f i))))))) -> (LinearIndependent.{max u3 u4, u1, u2} (Sigma.{u3, u4} η (fun (j : η) => ιs j)) R M (fun (ji : Sigma.{u3, u4} η (fun (j : η) => ιs j)) => f (Sigma.fst.{u3, u4} η (fun (j : η) => ιs j) ji) (Sigma.snd.{u3, u4} η (fun (j : η) => ιs j) ji)) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {η : Type.{u3}} {ιs : η -> Type.{u4}} {f : forall (j : η), (ιs j) -> M}, (forall (j : η), LinearIndependent.{u4, u1, u2} (ιs j) R M (f j) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (forall (i : η) (t : Set.{u3} η), (Set.Finite.{u3} η t) -> (Not (Membership.Mem.{u3, u3} η (Set.{u3} η) (Set.hasMem.{u3} η) i t)) -> (Disjoint.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) (Submodule.orderBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u4} M (ιs i) (f i))) (iSup.{u2, succ u3} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) η (fun (i : η) => iSup.{u2, 0} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) (Membership.Mem.{u3, u3} η (Set.{u3} η) (Set.hasMem.{u3} η) i t) (fun (H : Membership.Mem.{u3, u3} η (Set.{u3} η) (Set.hasMem.{u3} η) i t) => Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u4} M (ιs i) (f i))))))) -> (LinearIndependent.{max u3 u4, u1, u2} (Sigma.{u3, u4} η (fun (j : η) => ιs j)) R M (fun (ji : Sigma.{u3, u4} η (fun (j : η) => ιs j)) => f (Sigma.fst.{u3, u4} η (fun (j : η) => ιs j) ji) (Sigma.snd.{u3, u4} η (fun (j : η) => ιs j) ji)) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {η : Type.{u4}} {ιs : η -> Type.{u3}} {f : forall (j : η), (ιs j) -> M}, (forall (j : η), LinearIndependent.{u3, u2, u1} (ιs j) R M (f j) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (i : η) (t : Set.{u4} η), (Set.Finite.{u4} η t) -> (Not (Membership.mem.{u4, u4} η (Set.{u4} η) (Set.instMembershipSet.{u4} η) i t)) -> (Disjoint.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M (ιs i) (f i))) (supᵢ.{u1, succ u4} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))) η (fun (i : η) => supᵢ.{u1, 0} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))) (Membership.mem.{u4, u4} η (Set.{u4} η) (Set.instMembershipSet.{u4} η) i t) (fun (H : Membership.mem.{u4, u4} η (Set.{u4} η) (Set.instMembershipSet.{u4} η) i t) => Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M (ιs i) (f i))))))) -> (LinearIndependent.{max u4 u3, u2, u1} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R M (fun (ji : Sigma.{u4, u3} η (fun (j : η) => ιs j)) => f (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji) (Sigma.snd.{u4, u3} η (fun (j : η) => ιs j) ji)) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
-Case conversion may be inaccurate. Consider using '#align linear_independent_Union_finite linearIndependent_unionᵢ_finiteₓ'. -/
-theorem linearIndependent_unionᵢ_finite {η : Type _} {ιs : η → Type _} {f : ∀ j : η, ιs j → M}
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {η : Type.{u4}} {ιs : η -> Type.{u3}} {f : forall (j : η), (ιs j) -> M}, (forall (j : η), LinearIndependent.{u3, u2, u1} (ιs j) R M (f j) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (i : η) (t : Set.{u4} η), (Set.Finite.{u4} η t) -> (Not (Membership.mem.{u4, u4} η (Set.{u4} η) (Set.instMembershipSet.{u4} η) i t)) -> (Disjoint.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M (ιs i) (f i))) (iSup.{u1, succ u4} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))) η (fun (i : η) => iSup.{u1, 0} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))) (Membership.mem.{u4, u4} η (Set.{u4} η) (Set.instMembershipSet.{u4} η) i t) (fun (H : Membership.mem.{u4, u4} η (Set.{u4} η) (Set.instMembershipSet.{u4} η) i t) => Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M (ιs i) (f i))))))) -> (LinearIndependent.{max u4 u3, u2, u1} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R M (fun (ji : Sigma.{u4, u3} η (fun (j : η) => ιs j)) => f (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji) (Sigma.snd.{u4, u3} η (fun (j : η) => ιs j) ji)) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
+Case conversion may be inaccurate. Consider using '#align linear_independent_Union_finite linearIndependent_iUnion_finiteₓ'. -/
+theorem linearIndependent_iUnion_finite {η : Type _} {ιs : η → Type _} {f : ∀ j : η, ιs j → M}
     (hindep : ∀ j, LinearIndependent R (f j))
     (hd :
       ∀ i,
@@ -1076,14 +1076,14 @@ theorem linearIndependent_unionᵢ_finite {η : Type _} {ιs : η → Type _} {f
         apply
           disjoint_def.1 (hd x₁ {y₁} (finite_singleton y₁) fun h => h_cases (eq_of_mem_singleton h))
             (f x₁ x₂) (subset_span (mem_range_self _))
-        rw [supᵢ_singleton]
+        rw [iSup_singleton]
         simp only at hxy
         rw [hxy]
         exact subset_span (mem_range_self y₂)
       exact False.elim ((hindep x₁).NeZero _ h0)
   rw [range_sigma_eq_Union_range]
-  apply linearIndependent_unionᵢ_finite_subtype (fun j => (hindep j).to_subtype_range) hd
-#align linear_independent_Union_finite linearIndependent_unionᵢ_finite
+  apply linearIndependent_iUnion_finite_subtype (fun j => (hindep j).to_subtype_range) hd
+#align linear_independent_Union_finite linearIndependent_iUnion_finite
 
 end Subtype
 
@@ -1270,7 +1270,7 @@ theorem LinearIndependent.independent_span_singleton (hv : LinearIndependent R v
   refine' complete_lattice.independent_def.mp fun i => _
   rw [disjoint_iff_inf_le]
   intro m hm
-  simp only [mem_inf, mem_span_singleton, supᵢ_subtype', ← span_range_eq_supr] at hm
+  simp only [mem_inf, mem_span_singleton, iSup_subtype', ← span_range_eq_supr] at hm
   obtain ⟨⟨r, rfl⟩, hm⟩ := hm
   suffices r = 0 by simp [this]
   apply linear_independent_iff_not_smul_mem_span.mp hv i
@@ -1310,7 +1310,7 @@ theorem exists_maximal_independent' (s : ι → M) :
   have trans : Transitive r := fun I J K => Set.Subset.trans
   obtain ⟨⟨I, hli : indep I⟩, hmax : ∀ a, r ⟨I, hli⟩ a → r a ⟨I, hli⟩⟩ :=
     @exists_maximal_of_chains_bounded _ r
-      (fun c hc => ⟨⟨⋃ I ∈ c, (I : Set ι), key c hc⟩, fun I => Set.subset_bunionᵢ_of_mem⟩) trans
+      (fun c hc => ⟨⟨⋃ I ∈ c, (I : Set ι), key c hc⟩, fun I => Set.subset_biUnion_of_mem⟩) trans
   exact ⟨I, hli, fun J hsub hli => Set.Subset.antisymm hsub (hmax ⟨J, hli⟩ hsub)⟩
 #align exists_maximal_independent' exists_maximal_independent'
 
@@ -1885,7 +1885,7 @@ theorem exists_linearIndependent_extension (hs : LinearIndependent K (coe : s 
     exact subset_span (mem_insert _ _)
   · refine' fun c hc cc c0 => ⟨⋃₀ c, ⟨_, _⟩, fun x => _⟩
     · exact sUnion_subset fun x xc => (hc xc).1
-    · exact linearIndependent_unionₛ_of_directed cc.directed_on fun x xc => (hc xc).2
+    · exact linearIndependent_sUnion_of_directed cc.directed_on fun x xc => (hc xc).2
     · exact subset_sUnion_of_mem
 #align exists_linear_independent_extension exists_linearIndependent_extension

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -1095,7 +1095,7 @@ variable (hv : LinearIndependent R v)
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearEquiv.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearIndependent.totalEquiv._proof_1.{u2} R _inst_1) (LinearIndependent.totalEquiv._proof_2.{u2} R _inst_1) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))))
 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearEquiv.{u2, u2, max u2 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) x (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))))
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearEquiv.{u2, u2, max u2 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) x (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.total_equiv LinearIndependent.totalEquivₓ'. -/
 /-- Canonical isomorphism between linear combinations and the span of linearly independent vectors.
 -/
@@ -1120,7 +1120,7 @@ def LinearIndependent.totalEquiv (hv : LinearIndependent R v) : (ι →₀ R) 
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))))
 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearMap.{u2, u2, u3, max u2 u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) x (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))))
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearMap.{u2, u2, u3, max u2 u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) x (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr LinearIndependent.reprₓ'. -/
 /-- Linear combination representing a vector in the span of linearly independent vectors.
 
@@ -1135,7 +1135,7 @@ def LinearIndependent.repr (hv : LinearIndependent R v) : span R (range v) →
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))), Eq.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ 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(Ring.toSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u1, u3, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 v) (coeFn.{max (succ u3) (succ (max u1 u2)), max (succ u3) (succ (max u1 u2))} (LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R 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 but is expected to have type
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+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))), Eq.{succ u2} ((fun 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(Ring.toSemiring.{u1} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv) x)) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) x)
 Case conversion may be inaccurate. Consider using '#align linear_independent.total_repr LinearIndependent.total_reprₓ'. -/
 @[simp]
 theorem LinearIndependent.total_repr (x) : Finsupp.total ι M R v (hv.repr x) = x :=
@@ -1146,7 +1146,7 @@ theorem LinearIndependent.total_repr (x) : Finsupp.total ι M R v (hv.repr x) =
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5), Eq.{succ u3} (LinearMap.{u2, u2, u3, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) M (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) _inst_5) (LinearMap.comp.{u2, u2, u2, u3, max u1 u2, u3} R R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.right_ids.{u2, u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u1, u3, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 v) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Submodule.subtype.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} 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))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) M (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) _inst_5) (LinearMap.comp.{u1, u1, u1, u2, max u3 u1, u2} R R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} 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)))) (Finsupp.total.{u3, u2, u1} ι M R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 v) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Submodule.subtype.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} 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))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) M (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) _inst_5) (LinearMap.comp.{u1, u1, u1, u2, max u3 u1, u2} R R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} 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)))) (Finsupp.total.{u3, u2, u1} ι M R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 v) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Submodule.subtype.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))
 Case conversion may be inaccurate. Consider using '#align linear_independent.total_comp_repr LinearIndependent.total_comp_reprₓ'. -/
 theorem LinearIndependent.total_comp_repr :
     (Finsupp.total ι M R v).comp hv.repr = Submodule.subtype _ :=
@@ -1157,7 +1157,7 @@ theorem LinearIndependent.total_comp_repr :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5), Eq.{succ u3} (Submodule.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (LinearMap.ker.{u2, u2, u3, max u1 u2, max u3 u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.semilinearMapClass.{u2, u2, u3, max u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Bot.bot.{u3} (Submodule.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Submodule.hasBot.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5), Eq.{succ u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (LinearMap.ker.{u1, u1, u2, max u3 u1, max (max u3 u1) u2} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Bot.bot.{u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Submodule.instBotSubmodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))))
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5), Eq.{succ u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (LinearMap.ker.{u1, u1, u2, max u3 u1, max (max u3 u1) u2} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, max u1 u3} 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))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Bot.bot.{u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Submodule.instBotSubmodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_ker LinearIndependent.repr_kerₓ'. -/
 theorem LinearIndependent.repr_ker : hv.repr.ker = ⊥ := by
   rw [LinearIndependent.repr, LinearEquiv.ker]
@@ -1167,7 +1167,7 @@ theorem LinearIndependent.repr_ker : hv.repr.ker = ⊥ := by
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5), Eq.{succ (max u1 u2)} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.range.{u2, u2, u3, max u1 u2, max u3 u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.semilinearMapClass.{u2, u2, u3, max u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Top.top.{max u1 u2} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.hasTop.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5), Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.range.{u2, u2, u1, max u3 u2, max (max u3 u2) u1} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, max u2 u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Top.top.{max u3 u2} (Submodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.instTopSubmodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5), Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.range.{u2, u2, u1, max u3 u2, max (max u3 u2) u1} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, max u2 u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Top.top.{max u3 u2} (Submodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.instTopSubmodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_range LinearIndependent.repr_rangeₓ'. -/
 theorem LinearIndependent.repr_range : hv.repr.range = ⊤ := by
   rw [LinearIndependent.repr, LinearEquiv.range]
@@ -1177,7 +1177,7 @@ theorem LinearIndependent.repr_range : hv.repr.range = ⊤ := by
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) {l : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))} {x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) 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 but is expected to have type
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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv) x) l)
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 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq LinearIndependent.repr_eqₓ'. -/
 theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M R v l = ↑x) :
     hv.repr x = l :=
@@ -1199,7 +1199,7 @@ theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (i : ι) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))), (Eq.{succ u3} M ((fun (a : Type.{u3}) (b : 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(Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) 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(AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1)))))))))
 but is expected to have type
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(Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv) x) (Finsupp.single.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) i (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))))
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (i : ι) (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))), (Eq.{succ u2} M 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x 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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv) x) (Finsupp.single.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) i (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq_single LinearIndependent.repr_eq_singleₓ'. -/
 theorem LinearIndependent.repr_eq_single (i) (x) (hx : ↑x = v i) : hv.repr x = Finsupp.single i 1 :=
   by
@@ -1211,7 +1211,7 @@ theorem LinearIndependent.repr_eq_single (i) (x) (hx : ↑x = v i) : hv.repr x =
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) [_inst_8 : Nontrivial.{u2} R] (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))), Eq.{max (succ u3) 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(NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv) x))
 but is expected to have type
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(fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv) x))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) [_inst_8 : Nontrivial.{u2} R] (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι 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(fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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 Case conversion may be inaccurate. Consider using '#align linear_independent.span_repr_eq LinearIndependent.span_repr_eqₓ'. -/
 theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
     Span.repr R (Set.range v) x = (hv.repr x).equivMapDomain (Equiv.ofInjective _ hv.Injective) :=
@@ -1418,7 +1418,7 @@ open LinearMap
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {M' : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3)] {s : Set.{u2} M} {f : LinearMap.{u1, u1, u2, u3} 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))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6}, (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => 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(Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) s)) M' (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M') Type.{u3} (Set.hasCoeToSort.{u3} M') (Set.image.{u2, u3} M M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} 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))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} 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))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) 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(AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) s)))))) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_6)
 but is expected to have type
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-> (Disjoint.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 s) (LinearMap.ker.{u2, u2, u3, u1, max u3 u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) f)) -> (LinearIndependent.{u1, u2, u1} (Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) f) s)) R M' (fun (x : Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) f) s)) => Subtype.val.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Set.{u1} M') (Set.instMembershipSet.{u1} M') x (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') a) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) f) s)) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_6)
+  forall {R : Type.{u2}} {M : Type.{u3}} {M' : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_6 : Module.{u2, u1} R M' (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)] {s : Set.{u3} M} {f : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6}, (LinearIndependent.{u3, u2, u3} (Set.Elem.{u3} M s) R M (fun (x : Set.Elem.{u3} M s) => Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x s) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (Disjoint.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 s) (LinearMap.ker.{u2, u2, u3, u1, max u3 u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (LinearIndependent.{u1, u2, u1} (Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) R M' (fun (x : Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) => Subtype.val.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Set.{u1} M') (Set.instMembershipSet.{u1} M') x (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') a) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_6)
 Case conversion may be inaccurate. Consider using '#align linear_independent.image_subtype LinearIndependent.image_subtypeₓ'. -/
 theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
     (hs : LinearIndependent R (fun x => x : s → M)) (hf_inj : Disjoint (span R s) f.ker) :
@@ -1463,7 +1463,7 @@ theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv :
 lean 3 declaration is
   forall (G : Type.{u1}) [_inst_8 : Monoid.{u1} G] (L : Type.{u2}) [_inst_9 : CommRing.{u2} L] [_inst_10 : NoZeroDivisors.{u2} L (Distrib.toHasMul.{u2} L (Ring.toDistrib.{u2} L (CommRing.toRing.{u2} L _inst_9))) (MulZeroClass.toHasZero.{u2} L (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9))))))], LinearIndependent.{max u2 u1, u2, max u1 u2} (MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) => coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) (fun (_x : MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) => G -> L) (MonoidHom.hasCoeToFun.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) f) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9)) (Pi.addCommMonoid.{u1, u2} G (fun (ᾰ : G) => L) (fun (i : G) => AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) (Pi.Function.module.{u1, u2, u2} G L L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9)) (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9))))) (Semiring.toModule.{u2} L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9))))
 but is expected to have type
-  forall (G : Type.{u2}) [_inst_8 : Monoid.{u2} G] (L : Type.{u1}) [_inst_9 : CommRing.{u1} L] [_inst_10 : NoZeroDivisors.{u1} L (NonUnitalNonAssocRing.toMul.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))) (CommMonoidWithZero.toZero.{u1} L (CommSemiring.toCommMonoidWithZero.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))], LinearIndependent.{max u2 u1, u1, max u2 u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => L) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G _inst_8)) (MulOneClass.toMul.{u1} L (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (MonoidHom.monoidHomClass.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))))) f) (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (Pi.addCommMonoid.{u2, u1} G (fun (ᾰ : G) => L) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (Pi.module.{u2, u1, u1} G (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.14997 : G) => L) L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (fun (i : G) => Semiring.toModule.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9))))
+  forall (G : Type.{u2}) [_inst_8 : Monoid.{u2} G] (L : Type.{u1}) [_inst_9 : CommRing.{u1} L] [_inst_10 : NoZeroDivisors.{u1} L (NonUnitalNonAssocRing.toMul.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))) (CommMonoidWithZero.toZero.{u1} L (CommSemiring.toCommMonoidWithZero.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))], LinearIndependent.{max u2 u1, u1, max u2 u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => L) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) G L (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G _inst_8)) (MulOneClass.toMul.{u1} L (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))) G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9))))) (MonoidHom.monoidHomClass.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))))))) f) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)) (Pi.addCommMonoid.{u2, u1} G (fun (ᾰ : G) => L) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (Pi.module.{u2, u1, u1} G (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.14997 : G) => L) L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (fun (i : G) => Semiring.toModule.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_monoid_hom linearIndependent_monoidHomₓ'. -/
 -- See, for example, Keith Conrad's note
 --  <https://kconrad.math.uconn.edu/blurbs/galoistheory/linearchar.pdf>

bump to nightly-2023-05-03-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

aa7b8e08

Diff

@@ -207,7 +207,7 @@ theorem Fintype.linearIndependent_iff [Fintype ι] :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] [_inst_8 : Fintype.{u1} ι], Iff (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5) (Eq.{succ (max u1 u2)} (Submodule.{u2, max u1 u2} R (forall (i : ι), (fun (i : ι) => R) i) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i))) (LinearMap.ker.{u2, u2, max u1 u2, u3, max (max u1 u2) u3} R R (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (forall (i : ι), (fun (i : ι) => R) i) M (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5) (LinearMap.semilinearMapClass.{u2, u2, max u1 u2, u3} R R (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (coeFn.{max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3)), max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3))} (LinearEquiv.{0, 0, max u1 u2 u3, max (max u1 u2) u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (forall (i : ι), (fun (i : ι) => R) i) M (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5) (Pi.addCommMonoid.{u1, max u2 u3} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u1 u2, u3} R R (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u1, max u2 u3, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.module.{u2, u2, 0, u2, u3} R R Nat ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.module.{u2, u2, 0, max u1 u2, u3} R R Nat (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) (fun (_x : LinearEquiv.{0, 0, max u1 u2 u3, max (max u1 u2) u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (forall (i : ι), (fun (i : ι) => R) i) M (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5) (Pi.addCommMonoid.{u1, max u2 u3} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u1 u2, u3} R R (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u1, max u2 u3, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.module.{u2, u2, 0, u2, u3} R R Nat ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.module.{u2, u2, 0, max u1 u2, u3} R R Nat (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) => (forall (i : ι), LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) -> (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (forall (i : ι), (fun (i : ι) => R) i) M (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5)) (LinearEquiv.hasCoeToFun.{0, 0, max u1 u2 u3, max (max u1 u2) u3} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (forall (i : ι), (fun (i : ι) => R) i) M (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, max u2 u3} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u1 u2, u3} R R (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u1, max u2 u3, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.module.{u2, u2, 0, u2, u3} R R Nat ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.module.{u2, u2, 0, max u1 u2, u3} R R Nat (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)) (LinearMap.lsum.{u2, u3, u1, u2, 0} R M ι _inst_1 (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) Nat _inst_2 _inst_5 _inst_8 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u1} ι a b)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5))) (fun (i : ι) => LinearMap.smulRight.{u2, u2, u3, u2} R ((fun (i : ι) => R) i) M ((fun (i : ι) => R) i) _inst_1 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) _inst_5 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_1 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (IsScalarTower.left.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2))) (Module.toMulActionWithZero.{u2, u3} R M _inst_1 _inst_2 _inst_5))) (LinearMap.id.{u2, u2} R ((fun (i : ι) => R) i) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) (v i)))) (Bot.bot.{max u1 u2} (Submodule.{u2, max u1 u2} R (forall (i : ι), (fun (i : ι) => R) i) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i))) (Submodule.hasBot.{u2, max u1 u2} R (forall (i : ι), (fun (i : ι) => R) i) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] [_inst_8 : Fintype.{u3} ι], Iff (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) (Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.ker.{u2, u2, max u3 u2, u1, max (max u3 u2) u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (fun (i : ι) => LinearMap.smulRight.{u2, u2, u1, u2} R R M R _inst_1 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) _inst_5 (Semiring.toModule.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R _inst_1) _inst_5 (IsScalarTower.left.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (LinearMap.id.{u2, u2} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) 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(x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u1, 0, max (max u2 u3) u1, max (max u2 u3) u1} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (SemilinearMapClass.distribMulActionHomClass.{0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (LinearMap.lsum.{u2, u1, u3, u2, 0} R M ι _inst_1 (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) Nat _inst_2 _inst_5 _inst_8 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u3} ι a b)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (fun (i : ι) => LinearMap.smulRight.{u2, u2, u1, u2} R R M R _inst_1 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) _inst_5 (Semiring.toModule.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R _inst_1) _inst_5 (IsScalarTower.left.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (LinearMap.id.{u2, u2} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (v i)))) (Bot.bot.{max u3 u2} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (Submodule.instBotSubmodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] [_inst_8 : Fintype.{u3} ι], Iff (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) (Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.ker.{u2, u2, max u3 u2, u1, max (max u3 u2) u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun 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_inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun 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(Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (_x : forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun 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(Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) _x) (SMulHomClass.toFunLike.{max (max u2 u3) u1, 0, 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(Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u1, 0, max (max u2 u3) u1, max (max u2 u3) u1} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (SemilinearMapClass.distribMulActionHomClass.{0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (LinearMap.lsum.{u2, u1, u3, u2, 0} R M ι _inst_1 (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) Nat _inst_2 _inst_5 _inst_8 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u3} ι a b)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (fun (i : ι) => LinearMap.smulRight.{u2, u2, u1, u2} R R M R _inst_1 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) _inst_5 (Semiring.toModule.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R _inst_1) _inst_5 (IsScalarTower.left.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (LinearMap.id.{u2, u2} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (v i)))) (Bot.bot.{max u3 u2} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (Submodule.instBotSubmodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1440 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align fintype.linear_independent_iff' Fintype.linearIndependent_iff'ₓ'. -/
 /-- A finite family of vectors `v i` is linear independent iff the linear map that sends
 `c : ι → R` to `∑ i, c i • v i` has the trivial kernel. -/
@@ -790,7 +790,7 @@ theorem LinearIndependent.image {ι} {s : Set ι} {f : ι → M}
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {G : Type.{u4}} [hG : Group.{u4} G] [_inst_8 : DistribMulAction.{u4, u2} G R (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1))))] [_inst_9 : DistribMulAction.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))] [_inst_10 : IsScalarTower.{u4, u2, u3} G R M (SMulZeroClass.toHasSmul.{u4, u2} G R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1)))))) (DistribSMul.toSmulZeroClass.{u4, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{u4, u2} G R (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1)))) _inst_8))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)))) (SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u4, u2, u3} G R M (SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u1, u2, u3} ι R M (SMul.smul.{max u1 u4, max u1 u3} (ι -> G) (ι -> M) (Pi.smul'.{u1, u4, u3} ι (fun (ᾰ : ι) => G) (fun (ᾰ : ι) => M) (fun (i : ι) => SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9)))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)
 but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {G : Type.{u3}} [hG : Group.{u3} G] [_inst_8 : DistribMulAction.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))] [_inst_9 : DistribMulAction.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))] [_inst_10 : IsScalarTower.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u2} G R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (DistribSMul.toSMulZeroClass.{u3, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))) (DistribMulAction.toDistribSMul.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1))) _inst_8))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u4, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u4, u2, u1} ι R M (HSMul.hSMul.{max u4 u3, max u4 u1, max u4 u1} (ι -> G) (ι -> M) (ι -> M) (instHSMul.{max u4 u3, max u4 u1} (ι -> G) (ι -> M) (Pi.smul'.{u4, u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6795 : ι) => G) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6789 : ι) => M) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
+  forall {ι : Type.{u4}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {G : Type.{u3}} [hG : Group.{u3} G] [_inst_8 : DistribMulAction.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))] [_inst_9 : DistribMulAction.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))] [_inst_10 : IsScalarTower.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u2} G R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (DistribSMul.toSMulZeroClass.{u3, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))) (DistribMulAction.toDistribSMul.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1))) _inst_8))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u4, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u4, u2, u1} ι R M (HSMul.hSMul.{max u4 u3, max u4 u1, max u4 u1} (ι -> G) (ι -> M) (ι -> M) (instHSMul.{max u4 u3, max u4 u1} (ι -> G) (ι -> M) (Pi.smul'.{u4, u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6785 : ι) => G) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6779 : ι) => M) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent.group_smul LinearIndependent.group_smulₓ'. -/
 theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulAction G R]
     [DistribMulAction G M] [IsScalarTower G R M] [SMulCommClass G R M] {v : ι → M}
@@ -811,7 +811,7 @@ theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulActi
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {v : ι -> M}, (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall (w : ι -> (Units.{u2} R (Ring.toMonoid.{u2} R _inst_1))), LinearIndependent.{u1, u2, u3} ι R M (SMul.smul.{max u1 u2, max u1 u3} (ι -> (Units.{u2} R (Ring.toMonoid.{u2} R _inst_1))) (ι -> M) (Pi.smul'.{u1, u2, u3} ι (fun (ᾰ : ι) => Units.{u2} R (Ring.toMonoid.{u2} R _inst_1)) (fun (ᾰ : ι) => M) (fun (i : ι) => Units.hasSmul.{u2, u3} R M (Ring.toMonoid.{u2} R _inst_1) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {v : ι -> M}, (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))), LinearIndependent.{u3, u2, u1} ι R M (HSMul.hSMul.{max u3 u2, max u3 u1, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (ι -> M) (instHSMul.{max u3 u2, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.7025 : ι) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.7019 : ι) => M) (fun (i : ι) => Units.instSMulUnits.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {v : ι -> M}, (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))), LinearIndependent.{u3, u2, u1} ι R M (HSMul.hSMul.{max u3 u2, max u3 u1, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (ι -> M) (instHSMul.{max u3 u2, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.7015 : ι) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.7009 : ι) => M) (fun (i : ι) => Units.instSMulUnits.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent.units_smul LinearIndependent.units_smulₓ'. -/
 -- This lemma cannot be proved with `linear_independent.group_smul` since the action of
 -- `Rˣ` on `R` is not commutative.
@@ -1463,7 +1463,7 @@ theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv :
 lean 3 declaration is
   forall (G : Type.{u1}) [_inst_8 : Monoid.{u1} G] (L : Type.{u2}) [_inst_9 : CommRing.{u2} L] [_inst_10 : NoZeroDivisors.{u2} L (Distrib.toHasMul.{u2} L (Ring.toDistrib.{u2} L (CommRing.toRing.{u2} L _inst_9))) (MulZeroClass.toHasZero.{u2} L (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9))))))], LinearIndependent.{max u2 u1, u2, max u1 u2} (MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) => coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) (fun (_x : MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) => G -> L) (MonoidHom.hasCoeToFun.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) f) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9)) (Pi.addCommMonoid.{u1, u2} G (fun (ᾰ : G) => L) (fun (i : G) => AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) (Pi.Function.module.{u1, u2, u2} G L L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9)) (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9))))) (Semiring.toModule.{u2} L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9))))
 but is expected to have type
-  forall (G : Type.{u2}) [_inst_8 : Monoid.{u2} G] (L : Type.{u1}) [_inst_9 : CommRing.{u1} L] [_inst_10 : NoZeroDivisors.{u1} L (NonUnitalNonAssocRing.toMul.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))) (CommMonoidWithZero.toZero.{u1} L (CommSemiring.toCommMonoidWithZero.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))], LinearIndependent.{max u2 u1, u1, max u2 u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => L) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G _inst_8)) (MulOneClass.toMul.{u1} L (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (MonoidHom.monoidHomClass.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))))) f) (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (Pi.addCommMonoid.{u2, u1} G (fun (ᾰ : G) => L) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (Pi.module.{u2, u1, u1} G (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.15009 : G) => L) L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (fun (i : G) => Semiring.toModule.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9))))
+  forall (G : Type.{u2}) [_inst_8 : Monoid.{u2} G] (L : Type.{u1}) [_inst_9 : CommRing.{u1} L] [_inst_10 : NoZeroDivisors.{u1} L (NonUnitalNonAssocRing.toMul.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))) (CommMonoidWithZero.toZero.{u1} L (CommSemiring.toCommMonoidWithZero.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))], LinearIndependent.{max u2 u1, u1, max u2 u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => L) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G _inst_8)) (MulOneClass.toMul.{u1} L (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (MonoidHom.monoidHomClass.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))))) f) (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (Pi.addCommMonoid.{u2, u1} G (fun (ᾰ : G) => L) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (Pi.module.{u2, u1, u1} G (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.14997 : G) => L) L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (fun (i : G) => Semiring.toModule.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_monoid_hom linearIndependent_monoidHomₓ'. -/
 -- See, for example, Keith Conrad's note
 --  <https://kconrad.math.uconn.edu/blurbs/galoistheory/linearchar.pdf>

bump to nightly-2023-05-01-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b8ba04e2f326f3f7cf24ad129beda58531ada61

aad8b38f

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp, Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.linear_independent
-! leanprover-community/mathlib commit ef7acf407d265ad4081c8998687e994fa80ba70c
+! leanprover-community/mathlib commit 9d684a893c52e1d6692a504a118bfccbae04feeb
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -597,7 +597,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align linear_independent_iff_total_on linearIndependent_iff_totalOnₓ'. -/
 theorem linearIndependent_iff_totalOn {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔ (Finsupp.totalOn M M R id s).ker = ⊥ := by
-  rw [Finsupp.totalOn, LinearMap.ker, LinearMap.comap_codRestrict, map_bot, comap_bot,
+  rw [Finsupp.totalOn, LinearMap.ker, LinearMap.comap_codRestrict, Submodule.map_bot, comap_bot,
     LinearMap.ker_comp, linearIndependent_subtype_disjoint, disjoint_iff_inf_le, ←
     map_comap_subtype, map_le_iff_le_comap, comap_bot, ker_subtype, le_bot_iff]
 #align linear_independent_iff_total_on linearIndependent_iff_totalOn
@@ -1107,7 +1107,7 @@ def LinearIndependent.totalEquiv (hv : LinearIndependent R v) : (ι →₀ R) 
   · rw [← LinearMap.ker_eq_bot, LinearMap.ker_codRestrict]
     apply hv
   · rw [← LinearMap.range_eq_top, LinearMap.range_eq_map, LinearMap.map_codRestrict, ←
-      LinearMap.range_le_iff_comap, range_subtype, map_top]
+      LinearMap.range_le_iff_comap, range_subtype, Submodule.map_top]
     rw [Finsupp.range_total]
     exact le_rfl
   · intro l

bump to nightly-2023-04-27-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/9b2b58d6b14b895b2f375108e765cb47de71aebd

c8f7a684

Diff

@@ -790,7 +790,7 @@ theorem LinearIndependent.image {ι} {s : Set ι} {f : ι → M}
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {G : Type.{u4}} [hG : Group.{u4} G] [_inst_8 : DistribMulAction.{u4, u2} G R (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1))))] [_inst_9 : DistribMulAction.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))] [_inst_10 : IsScalarTower.{u4, u2, u3} G R M (SMulZeroClass.toHasSmul.{u4, u2} G R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1)))))) (DistribSMul.toSmulZeroClass.{u4, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{u4, u2} G R (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1)))) _inst_8))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)))) (SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u4, u2, u3} G R M (SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u1, u2, u3} ι R M (SMul.smul.{max u1 u4, max u1 u3} (ι -> G) (ι -> M) (Pi.smul'.{u1, u4, u3} ι (fun (ᾰ : ι) => G) (fun (ᾰ : ι) => M) (fun (i : ι) => SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9)))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)
 but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {G : Type.{u3}} [hG : Group.{u3} G] [_inst_8 : DistribMulAction.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))] [_inst_9 : DistribMulAction.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))] [_inst_10 : IsScalarTower.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u2} G R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (DistribSMul.toSMulZeroClass.{u3, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))) (DistribMulAction.toDistribSMul.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1))) _inst_8))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u4, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u4, u2, u1} ι R M (HSMul.hSMul.{max u4 u3, max u4 u1, max u4 u1} (ι -> G) (ι -> M) (ι -> M) (instHSMul.{max u4 u3, max u4 u1} (ι -> G) (ι -> M) (Pi.smul'.{u4, u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6835 : ι) => G) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6829 : ι) => M) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
+  forall {ι : Type.{u4}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {G : Type.{u3}} [hG : Group.{u3} G] [_inst_8 : DistribMulAction.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))] [_inst_9 : DistribMulAction.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))] [_inst_10 : IsScalarTower.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u2} G R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (DistribSMul.toSMulZeroClass.{u3, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))) (DistribMulAction.toDistribSMul.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1))) _inst_8))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u4, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u4, u2, u1} ι R M (HSMul.hSMul.{max u4 u3, max u4 u1, max u4 u1} (ι -> G) (ι -> M) (ι -> M) (instHSMul.{max u4 u3, max u4 u1} (ι -> G) (ι -> M) (Pi.smul'.{u4, u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6795 : ι) => G) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6789 : ι) => M) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent.group_smul LinearIndependent.group_smulₓ'. -/
 theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulAction G R]
     [DistribMulAction G M] [IsScalarTower G R M] [SMulCommClass G R M] {v : ι → M}
@@ -811,7 +811,7 @@ theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulActi
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {v : ι -> M}, (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall (w : ι -> (Units.{u2} R (Ring.toMonoid.{u2} R _inst_1))), LinearIndependent.{u1, u2, u3} ι R M (SMul.smul.{max u1 u2, max u1 u3} (ι -> (Units.{u2} R (Ring.toMonoid.{u2} R _inst_1))) (ι -> M) (Pi.smul'.{u1, u2, u3} ι (fun (ᾰ : ι) => Units.{u2} R (Ring.toMonoid.{u2} R _inst_1)) (fun (ᾰ : ι) => M) (fun (i : ι) => Units.hasSmul.{u2, u3} R M (Ring.toMonoid.{u2} R _inst_1) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {v : ι -> M}, (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))), LinearIndependent.{u3, u2, u1} ι R M (HSMul.hSMul.{max u3 u2, max u3 u1, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (ι -> M) (instHSMul.{max u3 u2, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.7065 : ι) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.7059 : ι) => M) (fun (i : ι) => Units.instSMulUnits.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {v : ι -> M}, (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))), LinearIndependent.{u3, u2, u1} ι R M (HSMul.hSMul.{max u3 u2, max u3 u1, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (ι -> M) (instHSMul.{max u3 u2, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.7025 : ι) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.7019 : ι) => M) (fun (i : ι) => Units.instSMulUnits.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent.units_smul LinearIndependent.units_smulₓ'. -/
 -- This lemma cannot be proved with `linear_independent.group_smul` since the action of
 -- `Rˣ` on `R` is not commutative.
@@ -1095,7 +1095,7 @@ variable (hv : LinearIndependent R v)
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearEquiv.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearIndependent.totalEquiv._proof_1.{u2} R _inst_1) (LinearIndependent.totalEquiv._proof_2.{u2} R _inst_1) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))))
 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearEquiv.{u2, u2, max u2 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) x (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))))
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearEquiv.{u2, u2, max u2 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) x (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.total_equiv LinearIndependent.totalEquivₓ'. -/
 /-- Canonical isomorphism between linear combinations and the span of linearly independent vectors.
 -/
@@ -1120,7 +1120,7 @@ def LinearIndependent.totalEquiv (hv : LinearIndependent R v) : (ι →₀ R) 
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))))
 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearMap.{u2, u2, u3, max u2 u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) x (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)))
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearMap.{u2, u2, u3, max u2 u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) x (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr LinearIndependent.reprₓ'. -/
 /-- Linear combination representing a vector in the span of linearly independent vectors.
 
@@ -1135,7 +1135,7 @@ def LinearIndependent.repr (hv : LinearIndependent R v) : span R (range v) →
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))), Eq.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ 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 but is expected to have type
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u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv) x)) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) x)
 Case conversion may be inaccurate. Consider using '#align linear_independent.total_repr LinearIndependent.total_reprₓ'. -/
 @[simp]
 theorem LinearIndependent.total_repr (x) : Finsupp.total ι M R v (hv.repr x) = x :=
@@ -1146,7 +1146,7 @@ theorem LinearIndependent.total_repr (x) : Finsupp.total ι M R v (hv.repr x) =
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5), Eq.{succ u3} (LinearMap.{u2, u2, u3, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) M (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) _inst_5) (LinearMap.comp.{u2, u2, u2, u3, max u1 u2, u3} R R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.right_ids.{u2, u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u1, u3, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 v) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Submodule.subtype.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} 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))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) M (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) _inst_5) (LinearMap.comp.{u1, u1, u1, u2, max u3 u1, u2} R R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} 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)))) (Finsupp.total.{u3, u2, u1} ι M R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 v) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Submodule.subtype.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} 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))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) M (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) _inst_5) (LinearMap.comp.{u1, u1, u1, u2, max u3 u1, u2} R R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} 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)))) (Finsupp.total.{u3, u2, u1} ι M R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 v) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Submodule.subtype.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))
 Case conversion may be inaccurate. Consider using '#align linear_independent.total_comp_repr LinearIndependent.total_comp_reprₓ'. -/
 theorem LinearIndependent.total_comp_repr :
     (Finsupp.total ι M R v).comp hv.repr = Submodule.subtype _ :=
@@ -1157,7 +1157,7 @@ theorem LinearIndependent.total_comp_repr :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5), Eq.{succ u3} (Submodule.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (LinearMap.ker.{u2, u2, u3, max u1 u2, max u3 u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.semilinearMapClass.{u2, u2, u3, max u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Bot.bot.{u3} (Submodule.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Submodule.hasBot.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5), Eq.{succ u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (LinearMap.ker.{u1, u1, u2, max u3 u1, max (max u3 u1) u2} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, max u1 u3} 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))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Bot.bot.{u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Submodule.instBotSubmodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))))
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5), Eq.{succ u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (LinearMap.ker.{u1, u1, u2, max u3 u1, max (max u3 u1) u2} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Bot.bot.{u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Submodule.instBotSubmodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_ker LinearIndependent.repr_kerₓ'. -/
 theorem LinearIndependent.repr_ker : hv.repr.ker = ⊥ := by
   rw [LinearIndependent.repr, LinearEquiv.ker]
@@ -1167,7 +1167,7 @@ theorem LinearIndependent.repr_ker : hv.repr.ker = ⊥ := by
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5), Eq.{succ (max u1 u2)} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.range.{u2, u2, u3, max u1 u2, max u3 u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.semilinearMapClass.{u2, u2, u3, max u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Top.top.{max u1 u2} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.hasTop.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5), Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1))) (LinearMap.range.{u2, u2, u1, max u3 u2, max (max u3 u2) u1} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, max u2 u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1))) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Top.top.{max u3 u2} (Submodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1))) (Submodule.instTopSubmodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5), Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Top.top.{max u3 u2} (Submodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.instTopSubmodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_range LinearIndependent.repr_rangeₓ'. -/
 theorem LinearIndependent.repr_range : hv.repr.range = ⊤ := by
   rw [LinearIndependent.repr, LinearEquiv.range]
@@ -1177,7 +1177,7 @@ theorem LinearIndependent.repr_range : hv.repr.range = ⊤ := by
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) {l : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))} {x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) 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 but is expected to have type
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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv) x) l)
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq LinearIndependent.repr_eqₓ'. -/
 theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M R v l = ↑x) :
     hv.repr x = l :=
@@ -1199,7 +1199,7 @@ theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (i : ι) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))), (Eq.{succ u3} M ((fun (a : Type.{u3}) (b : 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(AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1)))))))))
 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv) x) (Finsupp.single.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) i (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq_single LinearIndependent.repr_eq_singleₓ'. -/
 theorem LinearIndependent.repr_eq_single (i) (x) (hx : ↑x = v i) : hv.repr x = Finsupp.single i 1 :=
   by
@@ -1211,7 +1211,7 @@ theorem LinearIndependent.repr_eq_single (i) (x) (hx : ↑x = v i) : hv.repr x =
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) [_inst_8 : Nontrivial.{u2} R] (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))), Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) (Set.range.{u3, succ u1} M ι v)) R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) (Span.repr.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v) x) (Finsupp.equivMapDomain.{u1, u3, u2} ι (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) (Set.range.{u3, succ u1} M ι v)) R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Equiv.ofInjective.{succ u1, u3} ι M v (LinearIndependent.injective.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 _inst_8 hv)) (coeFn.{max (succ u3) (succ (max u1 u2)), max (succ u3) (succ (max u1 u2))} (LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) -> (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))))) (LinearMap.hasCoeToFun.{u2, u2, u3, max u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} 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(NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv) x))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) [_inst_8 : Nontrivial.{u2} R] (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι 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(AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M 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(LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv) x))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) [_inst_8 : Nontrivial.{u2} R] (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι 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(fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv) x))
 Case conversion may be inaccurate. Consider using '#align linear_independent.span_repr_eq LinearIndependent.span_repr_eqₓ'. -/
 theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
     Span.repr R (Set.range v) x = (hv.repr x).equivMapDomain (Equiv.ofInjective _ hv.Injective) :=
@@ -1418,7 +1418,7 @@ open LinearMap
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {M' : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3)] {s : Set.{u2} M} {f : LinearMap.{u1, u1, u2, u3} 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))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6}, (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => 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 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (LinearIndependent.{u1, u2, u1} (Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) R M' (fun (x : Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) => Subtype.val.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Set.{u1} M') (Set.instMembershipSet.{u1} M') x (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') a) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_6)
+  forall {R : Type.{u2}} {M : Type.{u3}} {M' : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_6 : Module.{u2, u1} R M' (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)] {s : Set.{u3} M} {f : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6}, (LinearIndependent.{u3, u2, u3} (Set.Elem.{u3} M s) R M (fun (x : Set.Elem.{u3} M s) => Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x s) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (Disjoint.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 s) (LinearMap.ker.{u2, u2, u3, u1, max u3 u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) f)) -> (LinearIndependent.{u1, u2, u1} (Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) f) s)) R M' (fun (x : Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) f) s)) => Subtype.val.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Set.{u1} M') (Set.instMembershipSet.{u1} M') x (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') a) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) f) s)) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_6)
 Case conversion may be inaccurate. Consider using '#align linear_independent.image_subtype LinearIndependent.image_subtypeₓ'. -/
 theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
     (hs : LinearIndependent R (fun x => x : s → M)) (hf_inj : Disjoint (span R s) f.ker) :
@@ -1463,7 +1463,7 @@ theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv :
 lean 3 declaration is
   forall (G : Type.{u1}) [_inst_8 : Monoid.{u1} G] (L : Type.{u2}) [_inst_9 : CommRing.{u2} L] [_inst_10 : NoZeroDivisors.{u2} L (Distrib.toHasMul.{u2} L (Ring.toDistrib.{u2} L (CommRing.toRing.{u2} L _inst_9))) (MulZeroClass.toHasZero.{u2} L (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9))))))], LinearIndependent.{max u2 u1, u2, max u1 u2} (MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) => coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) (fun (_x : MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) => G -> L) (MonoidHom.hasCoeToFun.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) f) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9)) (Pi.addCommMonoid.{u1, u2} G (fun (ᾰ : G) => L) (fun (i : G) => AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) (Pi.Function.module.{u1, u2, u2} G L L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9)) (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9))))) (Semiring.toModule.{u2} L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9))))
 but is expected to have type
-  forall (G : Type.{u2}) [_inst_8 : Monoid.{u2} G] (L : Type.{u1}) [_inst_9 : CommRing.{u1} L] [_inst_10 : NoZeroDivisors.{u1} L (NonUnitalNonAssocRing.toMul.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9)))) (CommMonoidWithZero.toZero.{u1} L (CommSemiring.toCommMonoidWithZero.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))], LinearIndependent.{max u2 u1, u1, max u2 u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => L) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G _inst_8)) (MulOneClass.toMul.{u1} L (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (MonoidHom.monoidHomClass.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))))) f) (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (Pi.addCommMonoid.{u2, u1} G (fun (ᾰ : G) => L) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9)))))) (Pi.module.{u2, u1, u1} G (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.14954 : G) => L) L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9))))) (fun (i : G) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))
+  forall (G : Type.{u2}) [_inst_8 : Monoid.{u2} G] (L : Type.{u1}) [_inst_9 : CommRing.{u1} L] [_inst_10 : NoZeroDivisors.{u1} L (NonUnitalNonAssocRing.toMul.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))) (CommMonoidWithZero.toZero.{u1} L (CommSemiring.toCommMonoidWithZero.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))], LinearIndependent.{max u2 u1, u1, max u2 u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => L) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G _inst_8)) (MulOneClass.toMul.{u1} L (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (MonoidHom.monoidHomClass.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (NonAssocRing.toNonAssocSemiring.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))))) f) (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (Pi.addCommMonoid.{u2, u1} G (fun (ᾰ : G) => L) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (Pi.module.{u2, u1, u1} G (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.15009 : G) => L) L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (fun (i : G) => Semiring.toModule.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_monoid_hom linearIndependent_monoidHomₓ'. -/
 -- See, for example, Keith Conrad's note
 --  <https://kconrad.math.uconn.edu/blurbs/galoistheory/linearchar.pdf>

bump to nightly-2023-03-27-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1

0e4ebd8c

Diff

@@ -788,7 +788,7 @@ theorem LinearIndependent.image {ι} {s : Set ι} {f : ι → M}
 
 /- warning: linear_independent.group_smul -> LinearIndependent.group_smul is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {G : Type.{u4}} [hG : Group.{u4} G] [_inst_8 : DistribMulAction.{u4, u2} G R (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (NonAssocRing.toAddGroupWithOne.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))] [_inst_9 : DistribMulAction.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))] [_inst_10 : IsScalarTower.{u4, u2, u3} G R M (SMulZeroClass.toHasSmul.{u4, u2} G R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (NonAssocRing.toAddGroupWithOne.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (DistribSMul.toSmulZeroClass.{u4, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (NonAssocRing.toAddGroupWithOne.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{u4, u2} G R (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (NonAssocRing.toAddGroupWithOne.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) _inst_8))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)))) (SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u4, u2, u3} G R M (SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u1, u2, u3} ι R M (SMul.smul.{max u1 u4, max u1 u3} (ι -> G) (ι -> M) (Pi.smul'.{u1, u4, u3} ι (fun (ᾰ : ι) => G) (fun (ᾰ : ι) => M) (fun (i : ι) => SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9)))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {G : Type.{u4}} [hG : Group.{u4} G] [_inst_8 : DistribMulAction.{u4, u2} G R (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1))))] [_inst_9 : DistribMulAction.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))] [_inst_10 : IsScalarTower.{u4, u2, u3} G R M (SMulZeroClass.toHasSmul.{u4, u2} G R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1)))))) (DistribSMul.toSmulZeroClass.{u4, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{u4, u2} G R (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1)))) _inst_8))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)))) (SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u4, u2, u3} G R M (SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u1, u2, u3} ι R M (SMul.smul.{max u1 u4, max u1 u3} (ι -> G) (ι -> M) (Pi.smul'.{u1, u4, u3} ι (fun (ᾰ : ι) => G) (fun (ᾰ : ι) => M) (fun (i : ι) => SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9)))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)
 but is expected to have type
   forall {ι : Type.{u4}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {G : Type.{u3}} [hG : Group.{u3} G] [_inst_8 : DistribMulAction.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))] [_inst_9 : DistribMulAction.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))] [_inst_10 : IsScalarTower.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u2} G R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (DistribSMul.toSMulZeroClass.{u3, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))) (DistribMulAction.toDistribSMul.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1))) _inst_8))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u4, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u4, u2, u1} ι R M (HSMul.hSMul.{max u4 u3, max u4 u1, max u4 u1} (ι -> G) (ι -> M) (ι -> M) (instHSMul.{max u4 u3, max u4 u1} (ι -> G) (ι -> M) (Pi.smul'.{u4, u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6835 : ι) => G) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6829 : ι) => M) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent.group_smul LinearIndependent.group_smulₓ'. -/
@@ -1197,7 +1197,7 @@ theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M
 
 /- warning: linear_independent.repr_eq_single -> LinearIndependent.repr_eq_single is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (i : ι) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))), (Eq.{succ u3} M ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) M (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) M (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) M (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) 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(AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) -> (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))))) (LinearMap.hasCoeToFun.{u2, u2, u3, max u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv) x) (Finsupp.single.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) i (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R _inst_1)))))))))
 but is expected to have type
   forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (i : ι) (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))), (Eq.{succ u2} M (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) x) (v i)) -> (Eq.{max (succ u3) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u2, max (succ u3) (succ u1)} (LinearMap.{u1, u1, u2, max u1 u3} 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))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv) x) (Finsupp.single.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) i (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq_single LinearIndependent.repr_eq_singleₓ'. -/

bump to nightly-2023-03-18-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/02ba8949f486ebecf93fe7460f1ed0564b5e442c

73d15350

Diff

@@ -289,7 +289,7 @@ theorem LinearIndependent.coe_range (i : LinearIndependent R v) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {M' : Type.{u4}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u4} M'] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] [_inst_6 : Module.{u2, u4} R M' _inst_1 _inst_3], (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5) -> (forall {f : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6}, (Disjoint.{u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (SetLike.partialOrder.{u3, u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u2, u3} R M _inst_1 _inst_2 _inst_5)) (Submodule.orderBot.{u2, u3} R M _inst_1 _inst_2 _inst_5) (Submodule.span.{u2, u3} R M _inst_1 _inst_2 _inst_5 (Set.range.{u3, succ u1} M ι v)) (LinearMap.ker.{u2, u2, u3, u4, max u3 u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)) -> (LinearIndependent.{u1, u2, u4} ι R M' (Function.comp.{succ u1, succ u3, succ u4} ι M M' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
 but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3], (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5) -> (forall {f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6}, (Disjoint.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.completeLattice.{u3, u2} R M _inst_1 _inst_2 _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.span.{u3, u2} R M _inst_1 _inst_2 _inst_5 (Set.range.{u2, succ u4} M ι v)) (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
+  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3], (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5) -> (forall {f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6}, (Disjoint.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.completeLattice.{u3, u2} R M _inst_1 _inst_2 _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.span.{u3, u2} R M _inst_1 _inst_2 _inst_5 (Set.range.{u2, succ u4} M ι v)) (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
 Case conversion may be inaccurate. Consider using '#align linear_independent.map LinearIndependent.mapₓ'. -/
 /-- If `v` is a linearly independent family of vectors and the kernel of a linear map `f` is
 disjoint with the submodule spanned by the vectors of `v`, then `f ∘ v` is a linearly independent
@@ -405,7 +405,7 @@ theorem linearIndependent_image {ι} {s : Set ι} {f : ι → M} (hf : Set.InjOn
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2], (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5) -> (LinearIndependent.{u1, u2, u3} ι R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u2, u3} R M _inst_1 _inst_2 _inst_5)) (Submodule.span.{u2, u3} R M _inst_1 _inst_2 _inst_5 (Set.range.{u3, succ u1} M ι v))) (fun (i : ι) => Subtype.mk.{succ u3} M (fun (x : M) => Membership.Mem.{u3, u3} M (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u2, u3} R M _inst_1 _inst_2 _inst_5)) x (Submodule.span.{u2, u3} R M _inst_1 _inst_2 _inst_5 (Set.range.{u3, succ u1} M ι v))) (v i) (Submodule.subset_span.{u2, u3} R M _inst_1 _inst_2 _inst_5 (Set.range.{u3, succ u1} M ι v) (v i) (Set.mem_range_self.{u3, succ u1} M ι v i))) _inst_1 (Submodule.addCommMonoid.{u2, u3} R M _inst_1 _inst_2 _inst_5 (Submodule.span.{u2, u3} R M _inst_1 _inst_2 _inst_5 (Set.range.{u3, succ u1} M ι v))) (Submodule.module.{u2, u3} R M _inst_1 _inst_2 _inst_5 (Submodule.span.{u2, u3} R M _inst_1 _inst_2 _inst_5 (Set.range.{u3, succ u1} M ι v))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2], (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) -> (LinearIndependent.{u3, u2, u1} ι R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) x (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, succ u3} M ι v)))) (fun (i : ι) => Subtype.mk.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) x (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, succ u3} M ι v))) (v i) (Submodule.subset_span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, succ u3} M ι v) (v i) (Set.mem_range_self.{succ u3, u1} M ι v i))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, succ u3} M ι v))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, succ u3} M ι v))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2], (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) -> (LinearIndependent.{u3, u2, u1} ι R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_5)) x (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, succ u3} M ι v)))) (fun (i : ι) => Subtype.mk.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_5)) x (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, succ u3} M ι v))) (v i) (Submodule.subset_span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, succ u3} M ι v) (v i) (Set.mem_range_self.{succ u3, u1} M ι v i))) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, succ u3} M ι v))) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, succ u3} M ι v))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_span linearIndependent_spanₓ'. -/
 theorem linearIndependent_span (hs : LinearIndependent R v) :
     @LinearIndependent ι R (span R (range v)) (fun i : ι => ⟨v i, subset_span (mem_range_self i)⟩) _
@@ -417,7 +417,7 @@ theorem linearIndependent_span (hs : LinearIndependent R v) :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {m : Nat} (x : M) (v : (Fin m) -> M), (LinearIndependent.{0, u1, u2} (Fin m) R M v _inst_1 _inst_2 _inst_5) -> (forall (c : R) (y : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_5 (Set.range.{u2, 1} M (Fin m) v))), (Eq.{succ u2} M (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) (SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_5)))) c x) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_5 (Set.range.{u2, 1} M (Fin m) v))) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_5 (Set.range.{u2, 1} M (Fin m) v))) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_5 (Set.range.{u2, 1} M (Fin m) v))) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_5 (Set.range.{u2, 1} M (Fin m) v))) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_5)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_5 (Set.range.{u2, 1} M (Fin m) v))))))) y)) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))))) -> (Eq.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) -> (LinearIndependent.{0, u1, u2} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R M (Fin.cons.{u2} m (fun (ᾰ : Fin (Nat.succ m)) => M) x v) _inst_1 _inst_2 _inst_5)
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {m : Nat} (x : M) (v : (Fin m) -> M), (LinearIndependent.{0, u2, u1} (Fin m) R M v _inst_1 _inst_2 _inst_5) -> (forall (c : R) (y : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) x (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, 1} M (Fin m) v)))), (Eq.{succ u1} M (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)))) (HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) c x) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, 1} M (Fin m) v)))) y)) (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))) -> (Eq.{succ u2} R c (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))) -> (LinearIndependent.{0, u2, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R M (Fin.cons.{u1} m (fun (ᾰ : Fin (Nat.succ m)) => M) x v) _inst_1 _inst_2 _inst_5)
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {m : Nat} (x : M) (v : (Fin m) -> M), (LinearIndependent.{0, u2, u1} (Fin m) R M v _inst_1 _inst_2 _inst_5) -> (forall (c : R) (y : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_5)) x (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, 1} M (Fin m) v)))), (Eq.{succ u1} M (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)))) (HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) c x) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_5) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, 1} M (Fin m) v)))) y)) (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))) -> (Eq.{succ u2} R c (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))) -> (LinearIndependent.{0, u2, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R M (Fin.cons.{u1} m (fun (ᾰ : Fin (Nat.succ m)) => M) x v) _inst_1 _inst_2 _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent.fin_cons' LinearIndependent.fin_cons'ₓ'. -/
 /-- See `linear_independent.fin_cons` for a family of elements in a vector space. -/
 theorem LinearIndependent.fin_cons' {m : ℕ} (x : M) (v : Fin m → M) (hli : LinearIndependent R v)
@@ -507,7 +507,7 @@ section Subtype
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] {s : Set.{u1} ι}, Iff (LinearIndependent.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) R M (Function.comp.{succ u1, succ u1, succ u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι M v ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeSubtype.{succ u1} ι (fun (x : ι) => Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) x s))))))) _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), (Membership.Mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Submodule.setLike.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) l (Finsupp.supported.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s)) -> (Eq.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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 but is expected to have type
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) l (Finsupp.supported.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R 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_inst_1))) => M) l) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) l (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R 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+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, Iff (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))), (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) 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(MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) l (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (Finsupp.zero.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_comp_subtype linearIndependent_comp_subtypeₓ'. -/
 theorem linearIndependent_comp_subtype {s : Set ι} :
     LinearIndependent R (v ∘ coe : s → M) ↔
@@ -532,7 +532,7 @@ theorem linearIndependent_comp_subtype {s : Set ι} :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] {s : Set.{u1} ι}, Iff (Not (LinearIndependent.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) R M (Function.comp.{succ u1, succ u1, succ u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι M v ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeSubtype.{succ u1} ι (fun (x : ι) => Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) x s))))))) _inst_1 _inst_2 _inst_5)) (Exists.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (fun (f : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) => And (Membership.Mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Submodule.setLike.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) f (Finsupp.supported.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s)) (And (Eq.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R 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 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, Iff (Not (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5)) (Exists.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (f : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => And (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R 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+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, Iff (Not (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5)) (Exists.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (f : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => And (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R 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 Case conversion may be inaccurate. Consider using '#align linear_dependent_comp_subtype' linearDependent_comp_subtype'ₓ'. -/
 theorem linearDependent_comp_subtype' {s : Set ι} :
     ¬LinearIndependent R (v ∘ coe : s → M) ↔
@@ -544,7 +544,7 @@ theorem linearDependent_comp_subtype' {s : Set ι} :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] {s : Set.{u1} ι}, Iff (Not (LinearIndependent.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) R M (Function.comp.{succ u1, succ u1, succ u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι M v ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Submodule.setLike.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 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(AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2))) (Module.toMulActionWithZero.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (fun (_x : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) => ι -> R) (Finsupp.coeFun.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) f i) (v i))) (OfNat.ofNat.{u3} M 0 (OfNat.mk.{u3} M 0 (Zero.zero.{u3} M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2))))))) (Ne.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) f (OfNat.ofNat.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R 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 but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (Submodule.instSetLikeSubmodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) f (Finsupp.supported.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s)) (And (Eq.{succ u1} M (Finset.sum.{u1, u3} M ι _inst_2 (Finsupp.support.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) f) (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) M _inst_1 _inst_2 _inst_5))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, 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.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) f i) (v i))) (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))) (Ne.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) f (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.zero.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, Iff (Not (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5)) (Exists.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (f : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => And (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (Submodule.setLike.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) f (Finsupp.supported.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s)) (And (Eq.{succ u1} M (Finset.sum.{u1, u3} M ι _inst_2 (Finsupp.support.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) f) (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) M M (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) M (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) M (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) M (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) M _inst_1 _inst_2 _inst_5))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, 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.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) f i) (v i))) (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))) (Ne.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) f (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.zero.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))))))
 Case conversion may be inaccurate. Consider using '#align linear_dependent_comp_subtype linearDependent_comp_subtypeₓ'. -/
 /-- A version of `linear_dependent_comp_subtype'` with `finsupp.total` unfolded. -/
 theorem linearDependent_comp_subtype {s : Set ι} :
@@ -557,7 +557,7 @@ theorem linearDependent_comp_subtype {s : Set ι} :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M 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(Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) -> (Eq.{succ u2} M (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) (fun (_x : LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) => (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u2} R R (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_2 _inst_5 (id.{succ u2} M)) l) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))))) -> (Eq.{max (succ u2) (succ u1)} (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) l (OfNat.ofNat.{max u2 u1} (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) 0 (OfNat.mk.{max u2 u1} (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) 0 (Zero.zero.{max u2 u1} (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Finsupp.zero.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))))
 but is expected to have type
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.instSetLikeSubmodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_2 _inst_5 (id.{succ u2} M)) l) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u1) (succ u2)} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) l (OfNat.ofNat.{max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) 0 (Zero.toOfNat0.{max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Finsupp.zero.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M s) R M (fun (x : Set.Elem.{u2} M s) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) x) _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))), (Membership.mem.{max u1 u2, max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.setLike.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_2 _inst_5 (id.{succ u2} M)) l) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u1) (succ u2)} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) l (OfNat.ofNat.{max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) 0 (Zero.toOfNat0.{max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Finsupp.zero.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_subtype linearIndependent_subtypeₓ'. -/
 theorem linearIndependent_subtype {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
@@ -569,7 +569,7 @@ theorem linearIndependent_subtype {s : Set M} :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] {s : Set.{u1} ι}, Iff (LinearIndependent.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) R M (Function.comp.{succ u1, succ u1, succ u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι M v ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeSubtype.{succ u1} ι (fun (x : ι) => Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) x s))))))) _inst_1 _inst_2 _inst_5) (Disjoint.{max u1 u2} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Submodule.setLike.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) (Submodule.orderBot.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.supported.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s) (LinearMap.ker.{u2, u2, max u1 u2, u3, max (max u1 u2) u3} R R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5) (LinearMap.semilinearMapClass.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u3, u2} ι M R _inst_1 _inst_2 _inst_5 v)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, Iff (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5) (Disjoint.{max u2 u3} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Submodule.completeLattice.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.supported.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s) (LinearMap.ker.{u2, u2, max u3 u2, u1, max (max u3 u2) u1} R R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v)))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, Iff (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5) (Disjoint.{max u2 u3} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Submodule.completeLattice.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.supported.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s) (LinearMap.ker.{u2, u2, max u3 u2, u1, max (max u3 u2) u1} R R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v)))
 Case conversion may be inaccurate. Consider using '#align linear_independent_comp_subtype_disjoint linearIndependent_comp_subtype_disjointₓ'. -/
 theorem linearIndependent_comp_subtype_disjoint {s : Set ι} :
     LinearIndependent R (v ∘ coe : s → M) ↔
@@ -581,7 +581,7 @@ theorem linearIndependent_comp_subtype_disjoint {s : Set ι} :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x s))))) x) _inst_1 _inst_2 _inst_5) (Disjoint.{max u2 u1} (Submodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.partialOrder.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) (Submodule.setLike.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) (Submodule.orderBot.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s) (LinearMap.ker.{u1, u1, max u2 u1, u2, max u2 u1} R R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, u2} R R (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_2 _inst_5 (id.{succ u2} M))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M s) R M (fun (x : Set.Elem.{u2} M s) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) x) _inst_1 _inst_2 _inst_5) (Disjoint.{max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Submodule.completeLattice.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s) (LinearMap.ker.{u1, u1, max u1 u2, u2, max u1 u2} R R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_2 _inst_5 (id.{succ u2} M))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M s) R M (fun (x : Set.Elem.{u2} M s) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) x) _inst_1 _inst_2 _inst_5) (Disjoint.{max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Submodule.completeLattice.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s) (LinearMap.ker.{u1, u1, max u1 u2, u2, max u1 u2} R R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_2 _inst_5 (id.{succ u2} M))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_subtype_disjoint linearIndependent_subtype_disjointₓ'. -/
 theorem linearIndependent_subtype_disjoint {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
@@ -593,7 +593,7 @@ theorem linearIndependent_subtype_disjoint {s : Set M} :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) _inst_1 (Submodule.addCommMonoid.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)))))
 but is expected to have type
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(Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))) (LinearMap.ker.{u1, u1, max u1 u2, u2, max u1 u2} R R (Subtype.{succ (max u2 u1)} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (x : Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => Membership.mem.{max u2 u1, max u2 u1} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.instSetLikeSubmodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) x (Finsupp.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_5 (Set.image.{u2, u2} M M (id.{succ u2} M) s)))) _inst_1 _inst_1 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(Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (x : Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => Membership.mem.{max u2 u1, max u2 u1} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R 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_inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))) (Submodule.instBotSubmodule.{u1, max u1 u2} R (Subtype.{succ (max u2 u1)} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (x : Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => Membership.mem.{max u2 u1, max u2 u1} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R 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(AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M s) R M (fun (x : Set.Elem.{u2} M s) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) x) _inst_1 _inst_2 _inst_5) (Eq.{max (succ u1) (succ u2)} (Submodule.{u1, max u1 u2} R (Subtype.{succ (max u2 u1)} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (x : Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => Membership.mem.{max u2 u1, max u2 u1} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.setLike.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) x (Finsupp.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))) _inst_1 (Submodule.addCommMonoid.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R 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 Case conversion may be inaccurate. Consider using '#align linear_independent_iff_total_on linearIndependent_iff_totalOnₓ'. -/
 theorem linearIndependent_iff_totalOn {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔ (Finsupp.totalOn M M R id s).ker = ⊥ := by
@@ -909,7 +909,7 @@ section Subtype
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall {s : Set.{u1} ι} {t : Set.{u1} ι}, (Disjoint.{u1} (Set.{u1} ι) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} ι) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} ι) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} ι) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} ι) (Set.completeBooleanAlgebra.{u1} ι)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} ι) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} ι) (Set.booleanAlgebra.{u1} ι))) s t) -> (Disjoint.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.partialOrder.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.orderBot.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.image.{u1, u3} ι M v s)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.image.{u1, u3} ι M v t))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall {s : Set.{u3} ι} {t : 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)))))) s t) -> (Disjoint.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.image.{u3, u1} ι M v s)) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.image.{u3, u1} ι M v t))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall {s : Set.{u3} ι} {t : 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)))))) s t) -> (Disjoint.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.image.{u3, u1} ι M v s)) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.image.{u3, u1} ι M v t))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.disjoint_span_image LinearIndependent.disjoint_span_imageₓ'. -/
 theorem LinearIndependent.disjoint_span_image (hv : LinearIndependent R v) {s t : Set ι}
     (hs : Disjoint s t) : Disjoint (Submodule.span R <| v '' s) (Submodule.span R <| v '' t) :=
@@ -925,7 +925,7 @@ theorem LinearIndependent.disjoint_span_image (hv : LinearIndependent R v) {s t
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_8 : Nontrivial.{u2} R], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall {s : Set.{u1} ι} {x : ι}, (Not (Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) x s)) -> (Not (Membership.Mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (v x) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.image.{u1, u3} ι M v s)))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Nontrivial.{u2} R], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall {s : Set.{u3} ι} {x : ι}, (Not (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s)) -> (Not (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) (v x) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.image.{u3, u1} ι M v s)))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Nontrivial.{u2} R], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall {s : Set.{u3} ι} {x : ι}, (Not (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s)) -> (Not (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) (v x) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.image.{u3, u1} ι M v s)))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.not_mem_span_image LinearIndependent.not_mem_span_imageₓ'. -/
 theorem LinearIndependent.not_mem_span_image [Nontrivial R] (hv : LinearIndependent R v) {s : Set ι}
     {x : ι} (h : x ∉ s) : v x ∉ Submodule.span R (v '' s) :=
@@ -962,7 +962,7 @@ theorem LinearIndependent.total_ne_of_not_mem_support [Nontrivial R] (hv : Linea
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u4}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u4} M] [_inst_5 : Module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] {v : (Sum.{u1, u2} ι ι') -> M}, Iff (LinearIndependent.{max u1 u2, u3, u4} (Sum.{u1, u2} ι ι') R M v (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5) (And (LinearIndependent.{u1, u3, u4} ι R M (Function.comp.{succ u1, max (succ u1) (succ u2), succ u4} ι (Sum.{u1, u2} ι ι') M v (Sum.inl.{u1, u2} ι ι')) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5) (And (LinearIndependent.{u2, u3, u4} ι' R M (Function.comp.{succ u2, max (succ u1) (succ u2), succ u4} ι' (Sum.{u1, u2} ι ι') M v (Sum.inr.{u1, u2} ι ι')) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5) (Disjoint.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5) (SetLike.partialOrder.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5)) (Submodule.orderBot.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5) (Submodule.span.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5 (Set.range.{u4, succ u1} M ι (Function.comp.{succ u1, max (succ u1) (succ u2), succ u4} ι (Sum.{u1, u2} ι ι') M v (Sum.inl.{u1, u2} ι ι')))) (Submodule.span.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5 (Set.range.{u4, succ u2} M ι' (Function.comp.{succ u2, max (succ u1) (succ u2), succ u4} ι' (Sum.{u1, u2} ι ι') M v (Sum.inr.{u1, u2} ι ι')))))))
 but is expected to have type
-  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {v : (Sum.{u4, u3} ι ι') -> M}, Iff (LinearIndependent.{max u4 u3, u2, u1} (Sum.{u4, u3} ι ι') R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (And (LinearIndependent.{u4, u2, u1} ι R M (Function.comp.{succ u4, max (succ u4) (succ u3), succ u1} ι (Sum.{u4, u3} ι ι') M v (Sum.inl.{u4, u3} ι ι')) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (And (LinearIndependent.{u3, u2, u1} ι' R M (Function.comp.{succ u3, max (succ u4) (succ u3), succ u1} ι' (Sum.{u4, u3} ι ι') M v (Sum.inr.{u4, u3} ι ι')) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Disjoint.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u4} M ι (Function.comp.{succ u4, max (succ u4) (succ u3), succ u1} ι (Sum.{u4, u3} ι ι') M v (Sum.inl.{u4, u3} ι ι')))) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι' (Function.comp.{succ u3, max (succ u4) (succ u3), succ u1} ι' (Sum.{u4, u3} ι ι') M v (Sum.inr.{u4, u3} ι ι')))))))
+  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {v : (Sum.{u4, u3} ι ι') -> M}, Iff (LinearIndependent.{max u4 u3, u2, u1} (Sum.{u4, u3} ι ι') R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (And (LinearIndependent.{u4, u2, u1} ι R M (Function.comp.{succ u4, max (succ u4) (succ u3), succ u1} ι (Sum.{u4, u3} ι ι') M v (Sum.inl.{u4, u3} ι ι')) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (And (LinearIndependent.{u3, u2, u1} ι' R M (Function.comp.{succ u3, max (succ u4) (succ u3), succ u1} ι' (Sum.{u4, u3} ι ι') M v (Sum.inr.{u4, u3} ι ι')) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Disjoint.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u4} M ι (Function.comp.{succ u4, max (succ u4) (succ u3), succ u1} ι (Sum.{u4, u3} ι ι') M v (Sum.inl.{u4, u3} ι ι')))) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι' (Function.comp.{succ u3, max (succ u4) (succ u3), succ u1} ι' (Sum.{u4, u3} ι ι') M v (Sum.inr.{u4, u3} ι ι')))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_sum linearIndependent_sumₓ'. -/
 theorem linearIndependent_sum {v : Sum ι ι' → M} :
     LinearIndependent R v ↔
@@ -1003,7 +1003,7 @@ theorem linearIndependent_sum {v : Sum ι ι' → M} :
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u4}} {v : ι -> M} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u4} M] [_inst_5 : Module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] {v' : ι' -> M}, (LinearIndependent.{u1, u3, u4} ι R M v (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5) -> (LinearIndependent.{u2, u3, u4} ι' R M v' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5) -> (Disjoint.{u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5) (SetLike.partialOrder.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5)) (Submodule.orderBot.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5) (Submodule.span.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5 (Set.range.{u4, succ u1} M ι v)) (Submodule.span.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5 (Set.range.{u4, succ u2} M ι' v'))) -> (LinearIndependent.{max u1 u2, u3, u4} (Sum.{u1, u2} ι ι') R M (Sum.elim.{u1, u2, succ u4} ι ι' M v v') (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5)
 but is expected to have type
-  forall {ι : Type.{u4}} {ι' : Type.{u1}} {R : Type.{u3}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {v' : ι' -> M}, (LinearIndependent.{u4, u3, u2} ι R M v (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (LinearIndependent.{u1, u3, u2} ι' R M v' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (Disjoint.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u4} M ι v)) (Submodule.span.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u1} M ι' v'))) -> (LinearIndependent.{max u1 u4, u3, u2} (Sum.{u4, u1} ι ι') R M (Sum.elim.{u4, u1, succ u2} ι ι' M v v') (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)
+  forall {ι : Type.{u4}} {ι' : Type.{u1}} {R : Type.{u3}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {v' : ι' -> M}, (LinearIndependent.{u4, u3, u2} ι R M v (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (LinearIndependent.{u1, u3, u2} ι' R M v' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (Disjoint.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u4} M ι v)) (Submodule.span.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u1} M ι' v'))) -> (LinearIndependent.{max u1 u4, u3, u2} (Sum.{u4, u1} ι ι') R M (Sum.elim.{u4, u1, succ u2} ι ι' M v v') (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent.sum_type LinearIndependent.sum_typeₓ'. -/
 theorem LinearIndependent.sum_type {v' : ι' → M} (hv : LinearIndependent R v)
     (hv' : LinearIndependent R v')
@@ -1016,7 +1016,7 @@ theorem LinearIndependent.sum_type {v' : ι' → M} (hv : LinearIndependent R v)
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {s : Set.{u2} M} {t : Set.{u2} M}, (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x s))))) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) t) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) t) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) t) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) t) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) t) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) t) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x t))))) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (Disjoint.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) (Submodule.orderBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 s) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 t)) -> (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Union.union.{u2} (Set.{u2} M) (Set.hasUnion.{u2} M) s t)) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Union.union.{u2} (Set.{u2} M) (Set.hasUnion.{u2} M) s t)) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Union.union.{u2} (Set.{u2} M) (Set.hasUnion.{u2} M) s t)) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Union.union.{u2} (Set.{u2} M) (Set.hasUnion.{u2} M) s t)) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Union.union.{u2} (Set.{u2} M) (Set.hasUnion.{u2} M) s t)) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Union.union.{u2} (Set.{u2} M) (Set.hasUnion.{u2} M) s t)) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x (Union.union.{u2} (Set.{u2} M) (Set.hasUnion.{u2} M) s t)))))) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {s : Set.{u2} M} {t : Set.{u2} M}, (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M s) R M (fun (x : Set.Elem.{u2} M s) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M t) R M (fun (x : Set.Elem.{u2} M t) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x t) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (Disjoint.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 s) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 t)) -> (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M (Union.union.{u2} (Set.{u2} M) (Set.instUnionSet.{u2} M) s t)) R M (fun (x : Set.Elem.{u2} M (Union.union.{u2} (Set.{u2} M) (Set.instUnionSet.{u2} M) s t)) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (Union.union.{u2} (Set.{u2} M) (Set.instUnionSet.{u2} M) s t)) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {s : Set.{u2} M} {t : Set.{u2} M}, (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M s) R M (fun (x : Set.Elem.{u2} M s) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M t) R M (fun (x : Set.Elem.{u2} M t) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x t) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (Disjoint.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 s) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 t)) -> (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M (Union.union.{u2} (Set.{u2} M) (Set.instUnionSet.{u2} M) s t)) R M (fun (x : Set.Elem.{u2} M (Union.union.{u2} (Set.{u2} M) (Set.instUnionSet.{u2} M) s t)) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (Union.union.{u2} (Set.{u2} M) (Set.instUnionSet.{u2} M) s t)) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent.union LinearIndependent.unionₓ'. -/
 theorem LinearIndependent.union {s t : Set M} (hs : LinearIndependent R (fun x => x : s → M))
     (ht : LinearIndependent R (fun x => x : t → M)) (hst : Disjoint (span R s) (span R t)) :
@@ -1028,7 +1028,7 @@ theorem LinearIndependent.union {s t : Set M} (hs : LinearIndependent R (fun x =
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} {f : ι -> (Set.{u2} M)}, (forall (i : ι), LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (f i)) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (f i)) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (f i)) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (f i)) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (f i)) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (f i)) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x (f i)))))) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (forall (i : ι) (t : Set.{u3} ι), (Set.Finite.{u3} ι t) -> (Not (Membership.Mem.{u3, u3} ι (Set.{u3} ι) (Set.hasMem.{u3} ι) i t)) -> (Disjoint.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) (Submodule.orderBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (f i)) (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) ι (fun (i : ι) => supᵢ.{u2, 0} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) (Membership.Mem.{u3, u3} ι (Set.{u3} ι) (Set.hasMem.{u3} ι) i t) (fun (H : Membership.Mem.{u3, u3} ι (Set.{u3} ι) (Set.hasMem.{u3} ι) i t) => Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (f i)))))) -> (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))))))) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} {f : ι -> (Set.{u2} M)}, (forall (i : ι), LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M (f i)) R M (fun (x : Set.Elem.{u2} M (f i)) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (f i)) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (forall (i : ι) (t : Set.{u3} ι), (Set.Finite.{u3} ι t) -> (Not (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i t)) -> (Disjoint.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (f i)) (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) ι (fun (i : ι) => supᵢ.{u2, 0} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i t) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i t) => Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (f i)))))) -> (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) R M (fun (x : Set.Elem.{u2} M (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} {f : ι -> (Set.{u2} M)}, (forall (i : ι), LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M (f i)) R M (fun (x : Set.Elem.{u2} M (f i)) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (f i)) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (forall (i : ι) (t : Set.{u3} ι), (Set.Finite.{u3} ι t) -> (Not (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i t)) -> (Disjoint.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (f i)) (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) ι (fun (i : ι) => supᵢ.{u2, 0} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i t) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i t) => Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (f i)))))) -> (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) R M (fun (x : Set.Elem.{u2} M (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (Set.unionᵢ.{u2, succ u3} M ι (fun (i : ι) => f i))) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent_Union_finite_subtype linearIndependent_unionᵢ_finite_subtypeₓ'. -/
 theorem linearIndependent_unionᵢ_finite_subtype {ι : Type _} {f : ι → Set M}
     (hl : ∀ i, LinearIndependent R (fun x => x : f i → M))
@@ -1053,7 +1053,7 @@ theorem linearIndependent_unionᵢ_finite_subtype {ι : Type _} {f : ι → Set
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {η : Type.{u3}} {ιs : η -> Type.{u4}} {f : forall (j : η), (ιs j) -> M}, (forall (j : η), LinearIndependent.{u4, u1, u2} (ιs j) R M (f j) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (forall (i : η) (t : Set.{u3} η), (Set.Finite.{u3} η t) -> (Not (Membership.Mem.{u3, u3} η (Set.{u3} η) (Set.hasMem.{u3} η) i t)) -> (Disjoint.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) (Submodule.orderBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u4} M (ιs i) (f i))) (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) η (fun (i : η) => supᵢ.{u2, 0} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) (Membership.Mem.{u3, u3} η (Set.{u3} η) (Set.hasMem.{u3} η) i t) (fun (H : Membership.Mem.{u3, u3} η (Set.{u3} η) (Set.hasMem.{u3} η) i t) => Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u4} M (ιs i) (f i))))))) -> (LinearIndependent.{max u3 u4, u1, u2} (Sigma.{u3, u4} η (fun (j : η) => ιs j)) R M (fun (ji : Sigma.{u3, u4} η (fun (j : η) => ιs j)) => f (Sigma.fst.{u3, u4} η (fun (j : η) => ιs j) ji) (Sigma.snd.{u3, u4} η (fun (j : η) => ιs j) ji)) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {η : Type.{u4}} {ιs : η -> Type.{u3}} {f : forall (j : η), (ιs j) -> M}, (forall (j : η), LinearIndependent.{u3, u2, u1} (ιs j) R M (f j) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (i : η) (t : Set.{u4} η), (Set.Finite.{u4} η t) -> (Not (Membership.mem.{u4, u4} η (Set.{u4} η) (Set.instMembershipSet.{u4} η) i t)) -> (Disjoint.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M (ιs i) (f i))) (supᵢ.{u1, succ u4} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))) η (fun (i : η) => supᵢ.{u1, 0} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))) (Membership.mem.{u4, u4} η (Set.{u4} η) (Set.instMembershipSet.{u4} η) i t) (fun (H : Membership.mem.{u4, u4} η (Set.{u4} η) (Set.instMembershipSet.{u4} η) i t) => Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M (ιs i) (f i))))))) -> (LinearIndependent.{max u4 u3, u2, u1} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R M (fun (ji : Sigma.{u4, u3} η (fun (j : η) => ιs j)) => f (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji) (Sigma.snd.{u4, u3} η (fun (j : η) => ιs j) ji)) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {η : Type.{u4}} {ιs : η -> Type.{u3}} {f : forall (j : η), (ιs j) -> M}, (forall (j : η), LinearIndependent.{u3, u2, u1} (ιs j) R M (f j) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (i : η) (t : Set.{u4} η), (Set.Finite.{u4} η t) -> (Not (Membership.mem.{u4, u4} η (Set.{u4} η) (Set.instMembershipSet.{u4} η) i t)) -> (Disjoint.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M (ιs i) (f i))) (supᵢ.{u1, succ u4} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))) η (fun (i : η) => supᵢ.{u1, 0} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))) (Membership.mem.{u4, u4} η (Set.{u4} η) (Set.instMembershipSet.{u4} η) i t) (fun (H : Membership.mem.{u4, u4} η (Set.{u4} η) (Set.instMembershipSet.{u4} η) i t) => Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M (ιs i) (f i))))))) -> (LinearIndependent.{max u4 u3, u2, u1} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R M (fun (ji : Sigma.{u4, u3} η (fun (j : η) => ιs j)) => f (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji) (Sigma.snd.{u4, u3} η (fun (j : η) => ιs j) ji)) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent_Union_finite linearIndependent_unionᵢ_finiteₓ'. -/
 theorem linearIndependent_unionᵢ_finite {η : Type _} {ιs : η → Type _} {f : ∀ j : η, ιs j → M}
     (hindep : ∀ j, LinearIndependent R (f j))
@@ -1095,7 +1095,7 @@ variable (hv : LinearIndependent R v)
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearEquiv.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearIndependent.totalEquiv._proof_1.{u2} R _inst_1) (LinearIndependent.totalEquiv._proof_2.{u2} R _inst_1) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))))
 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearEquiv.{u2, u2, max u2 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) x (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))))
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearEquiv.{u2, u2, max u2 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) x (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.total_equiv LinearIndependent.totalEquivₓ'. -/
 /-- Canonical isomorphism between linear combinations and the span of linearly independent vectors.
 -/
@@ -1120,7 +1120,7 @@ def LinearIndependent.totalEquiv (hv : LinearIndependent R v) : (ι →₀ R) 
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))))
 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearMap.{u2, u2, u3, max u2 u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) x (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)))
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearMap.{u2, u2, u3, max u2 u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) x (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr LinearIndependent.reprₓ'. -/
 /-- Linear combination representing a vector in the span of linearly independent vectors.
 
@@ -1135,7 +1135,7 @@ def LinearIndependent.repr (hv : LinearIndependent R v) : span R (range v) →
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))), Eq.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ 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 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv) x)) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) x)
 Case conversion may be inaccurate. Consider using '#align linear_independent.total_repr LinearIndependent.total_reprₓ'. -/
 @[simp]
 theorem LinearIndependent.total_repr (x) : Finsupp.total ι M R v (hv.repr x) = x :=
@@ -1146,7 +1146,7 @@ theorem LinearIndependent.total_repr (x) : Finsupp.total ι M R v (hv.repr x) =
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5), Eq.{succ u3} (LinearMap.{u2, u2, u3, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) M (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) _inst_5) (LinearMap.comp.{u2, u2, u2, u3, max u1 u2, u3} R R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.right_ids.{u2, u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u1, u3, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 v) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Submodule.subtype.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} 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))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) M (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) _inst_5) (LinearMap.comp.{u1, u1, u1, u2, max u3 u1, u2} R R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} 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)))) (Finsupp.total.{u3, u2, u1} ι M R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 v) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Submodule.subtype.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} 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))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) M (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) _inst_5) (LinearMap.comp.{u1, u1, u1, u2, max u3 u1, u2} R R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} 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)))) (Finsupp.total.{u3, u2, u1} ι M R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 v) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Submodule.subtype.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))
 Case conversion may be inaccurate. Consider using '#align linear_independent.total_comp_repr LinearIndependent.total_comp_reprₓ'. -/
 theorem LinearIndependent.total_comp_repr :
     (Finsupp.total ι M R v).comp hv.repr = Submodule.subtype _ :=
@@ -1157,7 +1157,7 @@ theorem LinearIndependent.total_comp_repr :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5), Eq.{succ u3} (Submodule.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (LinearMap.ker.{u2, u2, u3, max u1 u2, max u3 u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.semilinearMapClass.{u2, u2, u3, max u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Bot.bot.{u3} (Submodule.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Submodule.hasBot.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5), Eq.{succ u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (LinearMap.ker.{u1, u1, u2, max u3 u1, max (max u3 u1) u2} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, max u1 u3} 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))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Bot.bot.{u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Submodule.instBotSubmodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))))
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5), Eq.{succ u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (LinearMap.ker.{u1, u1, u2, max u3 u1, max (max u3 u1) u2} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, max u1 u3} 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))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Bot.bot.{u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Submodule.instBotSubmodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_ker LinearIndependent.repr_kerₓ'. -/
 theorem LinearIndependent.repr_ker : hv.repr.ker = ⊥ := by
   rw [LinearIndependent.repr, LinearEquiv.ker]
@@ -1167,7 +1167,7 @@ theorem LinearIndependent.repr_ker : hv.repr.ker = ⊥ := by
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5), Eq.{succ (max u1 u2)} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.range.{u2, u2, u3, max u1 u2, max u3 u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R 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(Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.semilinearMapClass.{u2, u2, u3, max u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Top.top.{max u1 u2} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.hasTop.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5), Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1))) (LinearMap.range.{u2, u2, u1, max u3 u2, max (max u3 u2) u1} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, max u2 u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1))) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Top.top.{max u3 u2} (Submodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1))) (Submodule.instTopSubmodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5), Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1))) (LinearMap.range.{u2, u2, u1, max u3 u2, max (max u3 u2) u1} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, max u2 u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1))) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) 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(Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_range LinearIndependent.repr_rangeₓ'. -/
 theorem LinearIndependent.repr_range : hv.repr.range = ⊤ := by
   rw [LinearIndependent.repr, LinearEquiv.range]
@@ -1177,7 +1177,7 @@ theorem LinearIndependent.repr_range : hv.repr.range = ⊤ := by
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) {l : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))} {x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) 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 but is expected to have type
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+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) {l : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))} {x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R 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(AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R 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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv) x) l)
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq LinearIndependent.repr_eqₓ'. -/
 theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M R v l = ↑x) :
     hv.repr x = l :=
@@ -1199,7 +1199,7 @@ theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M
 lean 3 declaration is
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 but is expected to have type
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+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (i : ι) (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))), (Eq.{succ u2} M 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 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq_single LinearIndependent.repr_eq_singleₓ'. -/
 theorem LinearIndependent.repr_eq_single (i) (x) (hx : ↑x = v i) : hv.repr x = Finsupp.single i 1 :=
   by
@@ -1211,7 +1211,7 @@ theorem LinearIndependent.repr_eq_single (i) (x) (hx : ↑x = v i) : hv.repr x =
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) [_inst_8 : Nontrivial.{u2} R] (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))), Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) (Set.range.{u3, succ u1} M ι v)) R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) (Span.repr.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v) x) (Finsupp.equivMapDomain.{u1, u3, u2} ι (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) (Set.range.{u3, succ u1} M ι v)) R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Equiv.ofInjective.{succ u1, u3} ι M v (LinearIndependent.injective.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 _inst_8 hv)) (coeFn.{max (succ u3) (succ (max u1 u2)), max (succ u3) (succ (max u1 u2))} (LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) -> (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))))) (LinearMap.hasCoeToFun.{u2, u2, u3, max u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv) x))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) [_inst_8 : Nontrivial.{u2} R] (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))), Eq.{max (succ u2) (succ u1)} (Finsupp.{u1, u2} (Set.Elem.{u1} M (Set.range.{u1, succ u3} M ι v)) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Span.repr.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v) x) (Finsupp.equivMapDomain.{u3, u1, u2} ι (Set.Elem.{u1} M (Set.range.{u1, succ u3} M ι v)) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Equiv.ofInjective.{succ u3, u1} ι M v (LinearIndependent.injective.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 _inst_8 hv)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u1, max (succ u3) (succ u2)} (LinearMap.{u2, u2, u1, max u2 u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u1} M (fun (x : M) => 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(Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv) x))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) [_inst_8 : Nontrivial.{u2} R] (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))), Eq.{max (succ u2) (succ u1)} (Finsupp.{u1, u2} (Set.Elem.{u1} M (Set.range.{u1, succ u3} M ι v)) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Span.repr.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v) x) (Finsupp.equivMapDomain.{u3, u1, u2} ι (Set.Elem.{u1} M (Set.range.{u1, succ u3} M ι v)) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Equiv.ofInjective.{succ u3, u1} ι M v (LinearIndependent.injective.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 _inst_8 hv)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u1, max (succ u3) (succ u2)} (LinearMap.{u2, u2, u1, max u2 u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv) x))
 Case conversion may be inaccurate. Consider using '#align linear_independent.span_repr_eq LinearIndependent.span_repr_eqₓ'. -/
 theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
     Span.repr R (Set.range v) x = (hv.repr x).equivMapDomain (Equiv.ofInjective _ hv.Injective) :=
@@ -1232,7 +1232,7 @@ theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], Iff (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (forall (i : ι) (a : R), (Membership.Mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (SMul.smul.{u2, u3} R M (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)))) a (v i)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.image.{u1, u3} ι M v (SDiff.sdiff.{u1} (Set.{u1} ι) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} ι) (Set.booleanAlgebra.{u1} ι)) (Set.univ.{u1} ι) (Singleton.singleton.{u1, u1} ι (Set.{u1} ι) (Set.hasSingleton.{u1} ι) i))))) -> (Eq.{succ u2} R a (OfNat.ofNat.{u2} R 0 (OfNat.mk.{u2} R 0 (Zero.zero.{u2} R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))))))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], Iff (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (forall (i : ι) (a : R), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) (HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))) a (v i)) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.image.{u3, u1} ι M v (SDiff.sdiff.{u3} (Set.{u3} ι) (Set.instSDiffSet.{u3} ι) (Set.univ.{u3} ι) (Singleton.singleton.{u3, u3} ι (Set.{u3} ι) (Set.instSingletonSet.{u3} ι) i))))) -> (Eq.{succ u2} R a (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], Iff (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (forall (i : ι) (a : R), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) (HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))) a (v i)) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.image.{u3, u1} ι M v (SDiff.sdiff.{u3} (Set.{u3} ι) (Set.instSDiffSet.{u3} ι) (Set.univ.{u3} ι) (Singleton.singleton.{u3, u3} ι (Set.{u3} ι) (Set.instSingletonSet.{u3} ι) i))))) -> (Eq.{succ u2} R a (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_iff_not_smul_mem_span linearIndependent_iff_not_smul_mem_spanₓ'. -/
 -- TODO: why is this so slow?
 theorem linearIndependent_iff_not_smul_mem_span :
@@ -1318,7 +1318,7 @@ theorem exists_maximal_independent' (s : ι → M) :
 lean 3 declaration is
   forall {ι : Type.{u1}} (R : Type.{u2}) {M : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (s : ι -> M), Exists.{succ u1} (Set.{u1} ι) (fun (I : Set.{u1} ι) => And (LinearIndependent.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) I) R M (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) I) => s ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) I) ι (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) I) ι (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) I) ι (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) I) ι (coeSubtype.{succ u1} ι (fun (x : ι) => Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) x I))))) x)) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (forall (i : ι), (Not (Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) i I)) -> (Exists.{succ u2} R (fun (a : R) => And (Ne.{succ u2} R a (OfNat.ofNat.{u2} R 0 (OfNat.mk.{u2} R 0 (Zero.zero.{u2} R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))))))) (Membership.Mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (SMul.smul.{u2, u3} R M (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)))) a (s i)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.image.{u1, u3} ι M s I)))))))
 but is expected to have type
-  forall {ι : Type.{u3}} (R : Type.{u2}) {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (s : ι -> M), Exists.{succ u3} (Set.{u3} ι) (fun (I : Set.{u3} ι) => And (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι I) R M (fun (x : Set.Elem.{u3} ι I) => s (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x I) x)) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (forall (i : ι), (Not (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I)) -> (Exists.{succ u2} R (fun (a : R) => And (Ne.{succ u2} R a (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) (HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))) a (s i)) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.image.{u3, u1} ι M s I)))))))
+  forall {ι : Type.{u3}} (R : Type.{u2}) {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (s : ι -> M), Exists.{succ u3} (Set.{u3} ι) (fun (I : Set.{u3} ι) => And (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι I) R M (fun (x : Set.Elem.{u3} ι I) => s (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x I) x)) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (forall (i : ι), (Not (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I)) -> (Exists.{succ u2} R (fun (a : R) => And (Ne.{succ u2} R a (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) (HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))) a (s i)) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.image.{u3, u1} ι M s I)))))))
 Case conversion may be inaccurate. Consider using '#align exists_maximal_independent exists_maximal_independentₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » I) -/
 theorem exists_maximal_independent (s : ι → M) :
@@ -1363,7 +1363,7 @@ end repr
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u4}} {v : ι -> M} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u4} M] [_inst_5 : Module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] [_inst_8 : Nontrivial.{u3} R], (LinearIndependent.{u1, u3, u4} ι R M v (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5) -> (forall (f : Function.Embedding.{succ u2, succ u1} ι' ι), (HasSubset.Subset.{u4} (Set.{u4} M) (Set.hasSubset.{u4} M) (Set.range.{u4, succ u1} M ι v) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5) (Set.{u4} M) (HasLiftT.mk.{succ u4, succ u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5) (Set.{u4} M) (CoeTCₓ.coe.{succ u4, succ u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5) (Set.{u4} M) (SetLike.Set.hasCoeT.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5)))) (Submodule.span.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5 (Set.range.{u4, succ u2} M ι' (Function.comp.{succ u2, succ u1, succ u4} ι' ι M v (coeFn.{max 1 (succ u2) (succ u1), max (succ u2) (succ u1)} (Function.Embedding.{succ u2, succ u1} ι' ι) (fun (_x : Function.Embedding.{succ u2, succ u1} ι' ι) => ι' -> ι) (Function.Embedding.hasCoeToFun.{succ u2, succ u1} ι' ι) f)))))) -> (Function.Surjective.{succ u2, succ u1} ι' ι (coeFn.{max 1 (succ u2) (succ u1), max (succ u2) (succ u1)} (Function.Embedding.{succ u2, succ u1} ι' ι) (fun (_x : Function.Embedding.{succ u2, succ u1} ι' ι) => ι' -> ι) (Function.Embedding.hasCoeToFun.{succ u2, succ u1} ι' ι) f)))
 but is expected to have type
-  forall {ι : Type.{u4}} {ι' : Type.{u1}} {R : Type.{u3}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Nontrivial.{u3} R], (LinearIndependent.{u4, u3, u2} ι R M v (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (forall (f : Function.Embedding.{succ u1, succ u4} ι' ι), (HasSubset.Subset.{u2} (Set.{u2} M) (Set.instHasSubsetSet.{u2} M) (Set.range.{u2, succ u4} M ι v) (SetLike.coe.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u1} M ι' (Function.comp.{succ u1, succ u4, succ u2} ι' ι M v (FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (Function.Embedding.{succ u1, succ u4} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι') => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u1, succ u4} (Function.Embedding.{succ u1, succ u4} ι' ι) ι' ι (Function.instEmbeddingLikeEmbedding.{succ u1, succ u4} ι' ι)) f)))))) -> (Function.Surjective.{succ u1, succ u4} ι' ι (FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (Function.Embedding.{succ u1, succ u4} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι') => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u1, succ u4} (Function.Embedding.{succ u1, succ u4} ι' ι) ι' ι (Function.instEmbeddingLikeEmbedding.{succ u1, succ u4} ι' ι)) f)))
+  forall {ι : Type.{u4}} {ι' : Type.{u1}} {R : Type.{u3}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Nontrivial.{u3} R], (LinearIndependent.{u4, u3, u2} ι R M v (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (forall (f : Function.Embedding.{succ u1, succ u4} ι' ι), (HasSubset.Subset.{u2} (Set.{u2} M) (Set.instHasSubsetSet.{u2} M) (Set.range.{u2, succ u4} M ι v) (SetLike.coe.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u1} M ι' (Function.comp.{succ u1, succ u4, succ u2} ι' ι M v (FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (Function.Embedding.{succ u1, succ u4} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι') => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u1, succ u4} (Function.Embedding.{succ u1, succ u4} ι' ι) ι' ι (Function.instEmbeddingLikeEmbedding.{succ u1, succ u4} ι' ι)) f)))))) -> (Function.Surjective.{succ u1, succ u4} ι' ι (FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (Function.Embedding.{succ u1, succ u4} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι') => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u1, succ u4} (Function.Embedding.{succ u1, succ u4} ι' ι) ι' ι (Function.instEmbeddingLikeEmbedding.{succ u1, succ u4} ι' ι)) f)))
 Case conversion may be inaccurate. Consider using '#align surjective_of_linear_independent_of_span surjective_of_linearIndependent_of_spanₓ'. -/
 theorem surjective_of_linearIndependent_of_span [Nontrivial R] (hv : LinearIndependent R v)
     (f : ι' ↪ ι) (hss : range v ⊆ span R (range (v ∘ f))) : Surjective f :=
@@ -1392,7 +1392,7 @@ theorem surjective_of_linearIndependent_of_span [Nontrivial R] (hv : LinearIndep
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Nontrivial.{u1} R] {s : Set.{u2} M} {t : Set.{u2} M}, (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x s))))) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (HasSubset.Subset.{u2} (Set.{u2} M) (Set.hasSubset.{u2} M) t s) -> (HasSubset.Subset.{u2} (Set.{u2} M) (Set.hasSubset.{u2} M) s ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)))) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 t))) -> (Eq.{succ u2} (Set.{u2} M) s t)
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Nontrivial.{u2} R] {s : Set.{u1} M} {t : Set.{u1} M}, (LinearIndependent.{u1, u2, u1} (Set.Elem.{u1} M s) R M (fun (x : Set.Elem.{u1} M s) => Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x s) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (HasSubset.Subset.{u1} (Set.{u1} M) (Set.instHasSubsetSet.{u1} M) t s) -> (HasSubset.Subset.{u1} (Set.{u1} M) (Set.instHasSubsetSet.{u1} M) s (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 t))) -> (Eq.{succ u1} (Set.{u1} M) s t)
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Nontrivial.{u2} R] {s : Set.{u1} M} {t : Set.{u1} M}, (LinearIndependent.{u1, u2, u1} (Set.Elem.{u1} M s) R M (fun (x : Set.Elem.{u1} M s) => Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x s) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (HasSubset.Subset.{u1} (Set.{u1} M) (Set.instHasSubsetSet.{u1} M) t s) -> (HasSubset.Subset.{u1} (Set.{u1} M) (Set.instHasSubsetSet.{u1} M) s (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 t))) -> (Eq.{succ u1} (Set.{u1} M) s t)
 Case conversion may be inaccurate. Consider using '#align eq_of_linear_independent_of_span_subtype eq_of_linearIndependent_of_span_subtypeₓ'. -/
 theorem eq_of_linearIndependent_of_span_subtype [Nontrivial R] {s t : Set M}
     (hs : LinearIndependent R (fun x => x : s → M)) (h : t ⊆ s) (hst : s ⊆ span R t) : s = t :=
@@ -1418,7 +1418,7 @@ open LinearMap
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {M' : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3)] {s : Set.{u2} M} {f : LinearMap.{u1, u1, u2, u3} 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))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6}, (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x s))))) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (Disjoint.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) (Submodule.orderBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 s) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} 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))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R 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+  forall {R : Type.{u2}} {M : Type.{u3}} {M' : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_6 : Module.{u2, u1} R M' (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)] {s : Set.{u3} M} {f : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6}, (LinearIndependent.{u3, u2, u3} (Set.Elem.{u3} M s) R M (fun (x : Set.Elem.{u3} M s) => Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x s) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (Disjoint.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 s) (LinearMap.ker.{u2, u2, u3, u1, max u3 u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (LinearIndependent.{u1, u2, u1} (Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) R M' (fun (x : Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) => Subtype.val.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Set.{u1} M') (Set.instMembershipSet.{u1} M') x (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') a) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_6)
 Case conversion may be inaccurate. Consider using '#align linear_independent.image_subtype LinearIndependent.image_subtypeₓ'. -/
 theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
     (hs : LinearIndependent R (fun x => x : s → M)) (hf_inj : Disjoint (span R s) f.ker) :
@@ -1656,7 +1656,7 @@ open Submodule
 lean 3 declaration is
   forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : DivisionRing.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_4 : Module.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {s : Set.{u1} V} {x : V} {y : V}, (Membership.Mem.{u1, u1} V (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (SetLike.hasMem.{u1, u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) V (Submodule.setLike.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)) x (Submodule.span.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4 (Insert.insert.{u1, u1} V (Set.{u1} V) (Set.hasInsert.{u1} V) y s))) -> (Not (Membership.Mem.{u1, u1} V (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (SetLike.hasMem.{u1, u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) V (Submodule.setLike.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)) x (Submodule.span.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4 s))) -> (Membership.Mem.{u1, u1} V (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (SetLike.hasMem.{u1, u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) V (Submodule.setLike.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)) y (Submodule.span.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4 (Insert.insert.{u1, u1} V (Set.{u1} V) (Set.hasInsert.{u1} V) x s)))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {s : Set.{u2} V} {x : V} {y : V}, (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)) x (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 (Insert.insert.{u2, u2} V (Set.{u2} V) (Set.instInsertSet.{u2} V) y s))) -> (Not (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)) x (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 s))) -> (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)) y (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 (Insert.insert.{u2, u2} V (Set.{u2} V) (Set.instInsertSet.{u2} V) x s)))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {s : Set.{u2} V} {x : V} {y : V}, (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)) x (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 (Insert.insert.{u2, u2} V (Set.{u2} V) (Set.instInsertSet.{u2} V) y s))) -> (Not (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)) x (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 s))) -> (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)) y (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 (Insert.insert.{u2, u2} V (Set.{u2} V) (Set.instInsertSet.{u2} V) x s)))
 Case conversion may be inaccurate. Consider using '#align mem_span_insert_exchange mem_span_insert_exchangeₓ'. -/
 /- TODO: some of the following proofs can generalized with a zero_ne_one predicate type class
    (instead of a data containing type class) -/
@@ -1676,7 +1676,7 @@ theorem mem_span_insert_exchange :
 lean 3 declaration is
   forall {ι : Type.{u2}} {K : Type.{u3}} {V : Type.{u1}} [_inst_1 : DivisionRing.{u3} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_4 : Module.{u3, u1} K V (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {v : ι -> V}, Iff (LinearIndependent.{u2, u3, u1} ι K V v (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (forall (i : ι), Not (Membership.Mem.{u1, u1} V (Submodule.{u3, u1} K V (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (SetLike.hasMem.{u1, u1} (Submodule.{u3, u1} K V (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) V (Submodule.setLike.{u3, u1} K V (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)) (v i) (Submodule.span.{u3, u1} K V (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4 (Set.image.{u2, u1} ι V v (SDiff.sdiff.{u2} (Set.{u2} ι) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} ι) (Set.booleanAlgebra.{u2} ι)) (Set.univ.{u2} ι) (Singleton.singleton.{u2, u2} ι (Set.{u2} ι) (Set.hasSingleton.{u2} ι) i))))))
 but is expected to have type
-  forall {ι : Type.{u2}} {K : Type.{u1}} {V : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u3} V] [_inst_4 : Module.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] {v : ι -> V}, Iff (LinearIndependent.{u2, u1, u3} ι K V v (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (forall (i : ι), Not (Membership.mem.{u3, u3} V (Submodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4)) (v i) (Submodule.span.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4 (Set.image.{u2, u3} ι V v (SDiff.sdiff.{u2} (Set.{u2} ι) (Set.instSDiffSet.{u2} ι) (Set.univ.{u2} ι) (Singleton.singleton.{u2, u2} ι (Set.{u2} ι) (Set.instSingletonSet.{u2} ι) i))))))
+  forall {ι : Type.{u2}} {K : Type.{u1}} {V : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u3} V] [_inst_4 : Module.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] {v : ι -> V}, Iff (LinearIndependent.{u2, u1, u3} ι K V v (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (forall (i : ι), Not (Membership.mem.{u3, u3} V (Submodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) V (Submodule.setLike.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4)) (v i) (Submodule.span.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4 (Set.image.{u2, u3} ι V v (SDiff.sdiff.{u2} (Set.{u2} ι) (Set.instSDiffSet.{u2} ι) (Set.univ.{u2} ι) (Singleton.singleton.{u2, u2} ι (Set.{u2} ι) (Set.instSingletonSet.{u2} ι) i))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_iff_not_mem_span linearIndependent_iff_not_mem_spanₓ'. -/
 theorem linearIndependent_iff_not_mem_span :
     LinearIndependent K v ↔ ∀ i, v i ∉ span K (v '' (univ \ {i})) :=
@@ -1694,7 +1694,7 @@ theorem linearIndependent_iff_not_mem_span :
 lean 3 declaration is
   forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : DivisionRing.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_4 : Module.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {s : Set.{u1} V} {x : V}, (LinearIndependent.{u1, u2, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) K V (fun (b : coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (coeSubtype.{succ u1} V (fun (x : V) => Membership.Mem.{u1, u1} V (Set.{u1} V) (Set.hasMem.{u1} V) x s))))) b) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) -> (Not (Membership.Mem.{u1, u1} V (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (SetLike.hasMem.{u1, u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) V (Submodule.setLike.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)) x (Submodule.span.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4 s))) -> (LinearIndependent.{u1, u2, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) (Insert.insert.{u1, u1} V (Set.{u1} V) (Set.hasInsert.{u1} V) x s)) K V (fun (b : coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) (Insert.insert.{u1, u1} V (Set.{u1} V) (Set.hasInsert.{u1} V) x s)) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) (Insert.insert.{u1, u1} V (Set.{u1} V) (Set.hasInsert.{u1} V) x s)) V (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) (Insert.insert.{u1, u1} V (Set.{u1} V) (Set.hasInsert.{u1} V) x s)) V (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) (Insert.insert.{u1, u1} V (Set.{u1} V) (Set.hasInsert.{u1} V) x s)) V (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) (Insert.insert.{u1, u1} V (Set.{u1} V) (Set.hasInsert.{u1} V) x s)) V (coeSubtype.{succ u1} V (fun (x_1 : V) => Membership.Mem.{u1, u1} V (Set.{u1} V) (Set.hasMem.{u1} V) x_1 (Insert.insert.{u1, u1} V (Set.{u1} V) (Set.hasInsert.{u1} V) x s)))))) b) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {s : Set.{u2} V} {x : V}, (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} V s) K V (fun (b : Set.Elem.{u2} V s) => Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s) b) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) -> (Not (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)) x (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 s))) -> (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} V (Insert.insert.{u2, u2} V (Set.{u2} V) (Set.instInsertSet.{u2} V) x s)) K V (fun (b : Set.Elem.{u2} V (Insert.insert.{u2, u2} V (Set.{u2} V) (Set.instInsertSet.{u2} V) x s)) => Subtype.val.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x_1 (Insert.insert.{u2, u2} V (Set.{u2} V) (Set.instInsertSet.{u2} V) x s)) b) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {s : Set.{u2} V} {x : V}, (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} V s) K V (fun (b : Set.Elem.{u2} V s) => Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s) b) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) -> (Not (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)) x (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 s))) -> (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} V (Insert.insert.{u2, u2} V (Set.{u2} V) (Set.instInsertSet.{u2} V) x s)) K V (fun (b : Set.Elem.{u2} V (Insert.insert.{u2, u2} V (Set.{u2} V) (Set.instInsertSet.{u2} V) x s)) => Subtype.val.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x_1 (Insert.insert.{u2, u2} V (Set.{u2} V) (Set.instInsertSet.{u2} V) x s)) b) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)
 Case conversion may be inaccurate. Consider using '#align linear_independent.insert LinearIndependent.insertₓ'. -/
 theorem LinearIndependent.insert (hs : LinearIndependent K (fun b => b : s → V))
     (hx : x ∉ span K s) : LinearIndependent K (fun b => b : insert x s → V) :=
@@ -1709,7 +1709,7 @@ theorem LinearIndependent.insert (hs : LinearIndependent K (fun b => b : s → V
 lean 3 declaration is
   forall {ι : Type.{u2}} {K : Type.{u3}} {V : Type.{u1}} [_inst_1 : DivisionRing.{u3} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_4 : Module.{u3, u1} K V (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {v : ι -> V} {x : V}, Iff (LinearIndependent.{u2, u3, u1} (Option.{u2} ι) K V (fun (o : Option.{u2} ι) => Option.casesOn'.{u2, u1} ι V o x v) (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (And (LinearIndependent.{u2, u3, u1} ι K V v (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Not (Membership.Mem.{u1, u1} V (Submodule.{u3, u1} K V (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (SetLike.hasMem.{u1, u1} (Submodule.{u3, u1} K V (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) V (Submodule.setLike.{u3, u1} K V (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)) x (Submodule.span.{u3, u1} K V (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4 (Set.range.{u1, succ u2} V ι v)))))
 but is expected to have type
-  forall {ι : Type.{u2}} {K : Type.{u1}} {V : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u3} V] [_inst_4 : Module.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] {v : ι -> V} {x : V}, Iff (LinearIndependent.{u2, u1, u3} (Option.{u2} ι) K V (fun (o : Option.{u2} ι) => Option.casesOn'.{u2, u3} ι V o x v) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (And (LinearIndependent.{u2, u1, u3} ι K V v (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (Not (Membership.mem.{u3, u3} V (Submodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4)) x (Submodule.span.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4 (Set.range.{u3, succ u2} V ι v)))))
+  forall {ι : Type.{u2}} {K : Type.{u1}} {V : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u3} V] [_inst_4 : Module.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] {v : ι -> V} {x : V}, Iff (LinearIndependent.{u2, u1, u3} (Option.{u2} ι) K V (fun (o : Option.{u2} ι) => Option.casesOn'.{u2, u3} ι V o x v) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (And (LinearIndependent.{u2, u1, u3} ι K V v (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (Not (Membership.mem.{u3, u3} V (Submodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) V (Submodule.setLike.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4)) x (Submodule.span.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4 (Set.range.{u3, succ u2} V ι v)))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_option' linearIndependent_option'ₓ'. -/
 theorem linearIndependent_option' :
     LinearIndependent K (fun o => Option.casesOn' o x v : Option ι → V) ↔
@@ -1727,7 +1727,7 @@ theorem linearIndependent_option' :
 lean 3 declaration is
   forall {ι : Type.{u2}} {K : Type.{u3}} {V : Type.{u1}} [_inst_1 : DivisionRing.{u3} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_4 : Module.{u3, u1} K V (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {v : ι -> V} {x : V}, (LinearIndependent.{u2, u3, u1} ι K V v (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) -> (Not (Membership.Mem.{u1, u1} V (Submodule.{u3, u1} K V (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (SetLike.hasMem.{u1, u1} (Submodule.{u3, u1} K V (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) V (Submodule.setLike.{u3, u1} K V (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)) x (Submodule.span.{u3, u1} K V (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4 (Set.range.{u1, succ u2} V ι v)))) -> (LinearIndependent.{u2, u3, u1} (Option.{u2} ι) K V (fun (o : Option.{u2} ι) => Option.casesOn'.{u2, u1} ι V o x v) (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)
 but is expected to have type
-  forall {ι : Type.{u2}} {K : Type.{u1}} {V : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u3} V] [_inst_4 : Module.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] {v : ι -> V} {x : V}, (LinearIndependent.{u2, u1, u3} ι K V v (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) -> (Not (Membership.mem.{u3, u3} V (Submodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4)) x (Submodule.span.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4 (Set.range.{u3, succ u2} V ι v)))) -> (LinearIndependent.{u2, u1, u3} (Option.{u2} ι) K V (fun (o : Option.{u2} ι) => Option.casesOn'.{u2, u3} ι V o x v) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4)
+  forall {ι : Type.{u2}} {K : Type.{u1}} {V : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u3} V] [_inst_4 : Module.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] {v : ι -> V} {x : V}, (LinearIndependent.{u2, u1, u3} ι K V v (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) -> (Not (Membership.mem.{u3, u3} V (Submodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) V (Submodule.setLike.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4)) x (Submodule.span.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4 (Set.range.{u3, succ u2} V ι v)))) -> (LinearIndependent.{u2, u1, u3} (Option.{u2} ι) K V (fun (o : Option.{u2} ι) => Option.casesOn'.{u2, u3} ι V o x v) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4)
 Case conversion may be inaccurate. Consider using '#align linear_independent.option LinearIndependent.optionₓ'. -/
 theorem LinearIndependent.option (hv : LinearIndependent K v)
     (hx : x ∉ Submodule.span K (range v)) :
@@ -1739,7 +1739,7 @@ theorem LinearIndependent.option (hv : LinearIndependent K v)
 lean 3 declaration is
   forall {ι : Type.{u2}} {K : Type.{u3}} {V : Type.{u1}} [_inst_1 : DivisionRing.{u3} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_4 : Module.{u3, u1} K V (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {v : (Option.{u2} ι) -> V}, Iff (LinearIndependent.{u2, u3, u1} (Option.{u2} ι) K V v (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (And (LinearIndependent.{u2, u3, u1} ι K V (Function.comp.{succ u2, succ u2, succ u1} ι (Option.{u2} ι) V v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) ι (Option.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} ι (Option.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} ι (Option.{u2} ι) (coeOption.{u2} ι))))) (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Not (Membership.Mem.{u1, u1} V (Submodule.{u3, u1} K V (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (SetLike.hasMem.{u1, u1} (Submodule.{u3, u1} K V (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) V (Submodule.setLike.{u3, u1} K V (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)) (v (Option.none.{u2} ι)) (Submodule.span.{u3, u1} K V (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4 (Set.range.{u1, succ u2} V ι (Function.comp.{succ u2, succ u2, succ u1} ι (Option.{u2} ι) V v ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) ι (Option.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} ι (Option.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} ι (Option.{u2} ι) (coeOption.{u2} ι))))))))))
 but is expected to have type
-  forall {ι : Type.{u2}} {K : Type.{u1}} {V : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u3} V] [_inst_4 : Module.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] {v : (Option.{u2} ι) -> V}, Iff (LinearIndependent.{u2, u1, u3} (Option.{u2} ι) K V v (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (And (LinearIndependent.{u2, u1, u3} ι K V (Function.comp.{succ u2, succ u2, succ u3} ι (Option.{u2} ι) V v (Option.some.{u2} ι)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (Not (Membership.mem.{u3, u3} V (Submodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4)) (v (Option.none.{u2} ι)) (Submodule.span.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4 (Set.range.{u3, succ u2} V ι (Function.comp.{succ u2, succ u2, succ u3} ι (Option.{u2} ι) V v (Option.some.{u2} ι)))))))
+  forall {ι : Type.{u2}} {K : Type.{u1}} {V : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u3} V] [_inst_4 : Module.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] {v : (Option.{u2} ι) -> V}, Iff (LinearIndependent.{u2, u1, u3} (Option.{u2} ι) K V v (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (And (LinearIndependent.{u2, u1, u3} ι K V (Function.comp.{succ u2, succ u2, succ u3} ι (Option.{u2} ι) V v (Option.some.{u2} ι)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (Not (Membership.mem.{u3, u3} V (Submodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) V (Submodule.setLike.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4)) (v (Option.none.{u2} ι)) (Submodule.span.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4 (Set.range.{u3, succ u2} V ι (Function.comp.{succ u2, succ u2, succ u3} ι (Option.{u2} ι) V v (Option.some.{u2} ι)))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_option linearIndependent_optionₓ'. -/
 theorem linearIndependent_option {v : Option ι → V} :
     LinearIndependent K v ↔
@@ -1751,7 +1751,7 @@ theorem linearIndependent_option {v : Option ι → V} :
 lean 3 declaration is
   forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : DivisionRing.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_4 : Module.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} {s : Set.{u3} ι} {a : ι} {f : ι -> V}, (Not (Membership.Mem.{u3, u3} ι (Set.{u3} ι) (Set.hasMem.{u3} ι) a s)) -> (Iff (LinearIndependent.{u3, u2, u1} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) (Insert.insert.{u3, u3} ι (Set.{u3} ι) (Set.hasInsert.{u3} ι) a s)) K V (fun (x : coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) (Insert.insert.{u3, u3} ι (Set.{u3} ι) (Set.hasInsert.{u3} ι) a s)) => f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) (Insert.insert.{u3, u3} ι (Set.{u3} ι) (Set.hasInsert.{u3} ι) a s)) ι (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) (Insert.insert.{u3, u3} ι (Set.{u3} ι) (Set.hasInsert.{u3} ι) a s)) ι (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) (Insert.insert.{u3, u3} ι (Set.{u3} ι) (Set.hasInsert.{u3} ι) a s)) ι (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) (Insert.insert.{u3, u3} ι (Set.{u3} ι) (Set.hasInsert.{u3} ι) a s)) ι (coeSubtype.{succ u3} ι (fun (x : ι) => Membership.Mem.{u3, u3} ι (Set.{u3} ι) (Set.hasMem.{u3} ι) x (Insert.insert.{u3, u3} ι (Set.{u3} ι) (Set.hasInsert.{u3} ι) a s)))))) x)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (And (LinearIndependent.{u3, u2, u1} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) K V (fun (x : coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) => f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (coeSubtype.{succ u3} ι (fun (x : ι) => Membership.Mem.{u3, u3} ι (Set.{u3} ι) (Set.hasMem.{u3} ι) x s))))) x)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Not (Membership.Mem.{u1, u1} V (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (SetLike.hasMem.{u1, u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) V (Submodule.setLike.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)) (f a) (Submodule.span.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4 (Set.image.{u3, u1} ι V f s))))))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u3} V] [_inst_4 : Module.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] {ι : Type.{u2}} {s : Set.{u2} ι} {a : ι} {f : ι -> V}, (Not (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) a s)) -> (Iff (LinearIndependent.{u2, u1, u3} (Set.Elem.{u2} ι (Insert.insert.{u2, u2} ι (Set.{u2} ι) (Set.instInsertSet.{u2} ι) a s)) K V (fun (x : Set.Elem.{u2} ι (Insert.insert.{u2, u2} ι (Set.{u2} ι) (Set.instInsertSet.{u2} ι) a s)) => f (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x (Insert.insert.{u2, u2} ι (Set.{u2} ι) (Set.instInsertSet.{u2} ι) a s)) x)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (And (LinearIndependent.{u2, u1, u3} (Set.Elem.{u2} ι s) K V (fun (x : Set.Elem.{u2} ι s) => f (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x s) x)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (Not (Membership.mem.{u3, u3} V (Submodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4)) (f a) (Submodule.span.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4 (Set.image.{u2, u3} ι V f s))))))
+  forall {K : Type.{u1}} {V : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u3} V] [_inst_4 : Module.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] {ι : Type.{u2}} {s : Set.{u2} ι} {a : ι} {f : ι -> V}, (Not (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) a s)) -> (Iff (LinearIndependent.{u2, u1, u3} (Set.Elem.{u2} ι (Insert.insert.{u2, u2} ι (Set.{u2} ι) (Set.instInsertSet.{u2} ι) a s)) K V (fun (x : Set.Elem.{u2} ι (Insert.insert.{u2, u2} ι (Set.{u2} ι) (Set.instInsertSet.{u2} ι) a s)) => f (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x (Insert.insert.{u2, u2} ι (Set.{u2} ι) (Set.instInsertSet.{u2} ι) a s)) x)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (And (LinearIndependent.{u2, u1, u3} (Set.Elem.{u2} ι s) K V (fun (x : Set.Elem.{u2} ι s) => f (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x s) x)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (Not (Membership.mem.{u3, u3} V (Submodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4) V (Submodule.setLike.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4)) (f a) (Submodule.span.{u1, u3} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_4 (Set.image.{u2, u3} ι V f s))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_insert' linearIndependent_insert'ₓ'. -/
 theorem linearIndependent_insert' {ι} {s : Set ι} {a : ι} {f : ι → V} (has : a ∉ s) :
     (LinearIndependent K fun x : insert a s => f x) ↔
@@ -1766,7 +1766,7 @@ theorem linearIndependent_insert' {ι} {s : Set ι} {a : ι} {f : ι → V} (has
 lean 3 declaration is
   forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : DivisionRing.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_4 : Module.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {s : Set.{u1} V} {x : V}, (Not (Membership.Mem.{u1, u1} V (Set.{u1} V) (Set.hasMem.{u1} V) x s)) -> (Iff (LinearIndependent.{u1, u2, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) (Insert.insert.{u1, u1} V (Set.{u1} V) (Set.hasInsert.{u1} V) x s)) K V (fun (b : coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) (Insert.insert.{u1, u1} V (Set.{u1} V) (Set.hasInsert.{u1} V) x s)) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) (Insert.insert.{u1, u1} V (Set.{u1} V) (Set.hasInsert.{u1} V) x s)) V (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) (Insert.insert.{u1, u1} V (Set.{u1} V) (Set.hasInsert.{u1} V) x s)) V (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) (Insert.insert.{u1, u1} V (Set.{u1} V) (Set.hasInsert.{u1} V) x s)) V (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) (Insert.insert.{u1, u1} V (Set.{u1} V) (Set.hasInsert.{u1} V) x s)) V (coeSubtype.{succ u1} V (fun (x_1 : V) => Membership.Mem.{u1, u1} V (Set.{u1} V) (Set.hasMem.{u1} V) x_1 (Insert.insert.{u1, u1} V (Set.{u1} V) (Set.hasInsert.{u1} V) x s)))))) b) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (And (LinearIndependent.{u1, u2, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) K V (fun (b : coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (coeSubtype.{succ u1} V (fun (x : V) => Membership.Mem.{u1, u1} V (Set.{u1} V) (Set.hasMem.{u1} V) x s))))) b) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Not (Membership.Mem.{u1, u1} V (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (SetLike.hasMem.{u1, u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) V (Submodule.setLike.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)) x (Submodule.span.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4 s)))))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {s : Set.{u2} V} {x : V}, (Not (Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s)) -> (Iff (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} V (Insert.insert.{u2, u2} V (Set.{u2} V) (Set.instInsertSet.{u2} V) x s)) K V (fun (b : Set.Elem.{u2} V (Insert.insert.{u2, u2} V (Set.{u2} V) (Set.instInsertSet.{u2} V) x s)) => Subtype.val.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x_1 (Insert.insert.{u2, u2} V (Set.{u2} V) (Set.instInsertSet.{u2} V) x s)) b) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (And (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} V s) K V (fun (b : Set.Elem.{u2} V s) => Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s) b) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Not (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)) x (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 s)))))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {s : Set.{u2} V} {x : V}, (Not (Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s)) -> (Iff (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} V (Insert.insert.{u2, u2} V (Set.{u2} V) (Set.instInsertSet.{u2} V) x s)) K V (fun (b : Set.Elem.{u2} V (Insert.insert.{u2, u2} V (Set.{u2} V) (Set.instInsertSet.{u2} V) x s)) => Subtype.val.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x_1 (Insert.insert.{u2, u2} V (Set.{u2} V) (Set.instInsertSet.{u2} V) x s)) b) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (And (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} V s) K V (fun (b : Set.Elem.{u2} V s) => Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s) b) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Not (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)) x (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 s)))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_insert linearIndependent_insertₓ'. -/
 theorem linearIndependent_insert (hxs : x ∉ s) :
     (LinearIndependent K fun b : insert x s => (b : V)) ↔
@@ -1790,7 +1790,7 @@ theorem linearIndependent_pair {x y : V} (hx : x ≠ 0) (hy : ∀ a : K, a • x
 lean 3 declaration is
   forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : DivisionRing.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_4 : Module.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {x : V} {n : Nat} {v : (Fin n) -> V}, Iff (LinearIndependent.{0, u2, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) K V (Fin.cons.{u1} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => V) x v) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (And (LinearIndependent.{0, u2, u1} (Fin n) K V v (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Not (Membership.Mem.{u1, u1} V (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (SetLike.hasMem.{u1, u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) V (Submodule.setLike.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)) x (Submodule.span.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4 (Set.range.{u1, 1} V (Fin n) v)))))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {x : V} {n : Nat} {v : (Fin n) -> V}, Iff (LinearIndependent.{0, u1, u2} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) K V (Fin.cons.{u2} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => V) x v) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (And (LinearIndependent.{0, u1, u2} (Fin n) K V v (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Not (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)) x (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 (Set.range.{u2, 1} V (Fin n) v)))))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {x : V} {n : Nat} {v : (Fin n) -> V}, Iff (LinearIndependent.{0, u1, u2} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) K V (Fin.cons.{u2} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => V) x v) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (And (LinearIndependent.{0, u1, u2} (Fin n) K V v (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Not (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)) x (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 (Set.range.{u2, 1} V (Fin n) v)))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_fin_cons linearIndependent_fin_consₓ'. -/
 theorem linearIndependent_fin_cons {n} {v : Fin n → V} :
     LinearIndependent K (Fin.cons x v : Fin (n + 1) → V) ↔
@@ -1809,7 +1809,7 @@ theorem linearIndependent_fin_cons {n} {v : Fin n → V} :
 lean 3 declaration is
   forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : DivisionRing.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_4 : Module.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {x : V} {n : Nat} {v : (Fin n) -> V}, Iff (LinearIndependent.{0, u2, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) K V (Fin.snoc.{u1} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => V) v x) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (And (LinearIndependent.{0, u2, u1} (Fin n) K V v (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Not (Membership.Mem.{u1, u1} V (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (SetLike.hasMem.{u1, u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) V (Submodule.setLike.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)) x (Submodule.span.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4 (Set.range.{u1, 1} V (Fin n) v)))))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {x : V} {n : Nat} {v : (Fin n) -> V}, Iff (LinearIndependent.{0, u1, u2} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) K V (Fin.snoc.{u2} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => V) v x) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (And (LinearIndependent.{0, u1, u2} (Fin n) K V v (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Not (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)) x (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 (Set.range.{u2, 1} V (Fin n) v)))))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {x : V} {n : Nat} {v : (Fin n) -> V}, Iff (LinearIndependent.{0, u1, u2} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) K V (Fin.snoc.{u2} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => V) v x) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (And (LinearIndependent.{0, u1, u2} (Fin n) K V v (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Not (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)) x (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 (Set.range.{u2, 1} V (Fin n) v)))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_fin_snoc linearIndependent_fin_snocₓ'. -/
 theorem linearIndependent_fin_snoc {n} {v : Fin n → V} :
     LinearIndependent K (Fin.snoc v x : Fin (n + 1) → V) ↔
@@ -1821,7 +1821,7 @@ theorem linearIndependent_fin_snoc {n} {v : Fin n → V} :
 lean 3 declaration is
   forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : DivisionRing.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_4 : Module.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {x : V} {n : Nat} {v : (Fin n) -> V}, (LinearIndependent.{0, u2, u1} (Fin n) K V v (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) -> (Not (Membership.Mem.{u1, u1} V (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (SetLike.hasMem.{u1, u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) V (Submodule.setLike.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)) x (Submodule.span.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4 (Set.range.{u1, 1} V (Fin n) v)))) -> (LinearIndependent.{0, u2, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) K V (Fin.cons.{u1} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => V) x v) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {x : V} {n : Nat} {v : (Fin n) -> V}, (LinearIndependent.{0, u1, u2} (Fin n) K V v (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) -> (Not (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)) x (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 (Set.range.{u2, 1} V (Fin n) v)))) -> (LinearIndependent.{0, u1, u2} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) K V (Fin.cons.{u2} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => V) x v) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {x : V} {n : Nat} {v : (Fin n) -> V}, (LinearIndependent.{0, u1, u2} (Fin n) K V v (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) -> (Not (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)) x (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 (Set.range.{u2, 1} V (Fin n) v)))) -> (LinearIndependent.{0, u1, u2} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) K V (Fin.cons.{u2} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => V) x v) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)
 Case conversion may be inaccurate. Consider using '#align linear_independent.fin_cons LinearIndependent.fin_consₓ'. -/
 /-- See `linear_independent.fin_cons'` for an uglier version that works if you
 only have a module over a semiring. -/
@@ -1834,7 +1834,7 @@ theorem LinearIndependent.fin_cons {n} {v : Fin n → V} (hv : LinearIndependent
 lean 3 declaration is
   forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : DivisionRing.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_4 : Module.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {n : Nat} {v : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> V}, Iff (LinearIndependent.{0, u2, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) K V v (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (And (LinearIndependent.{0, u2, u1} (Fin n) K V (Fin.tail.{u1} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => V) v) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Not (Membership.Mem.{u1, u1} V (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (SetLike.hasMem.{u1, u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) V (Submodule.setLike.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)) (v (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (Submodule.span.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4 (Set.range.{u1, 1} V (Fin n) (Fin.tail.{u1} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => V) v))))))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {n : Nat} {v : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> V}, Iff (LinearIndependent.{0, u1, u2} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) K V v (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (And (LinearIndependent.{0, u1, u2} (Fin n) K V (Fin.tail.{u2} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => V) v) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Not (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)) (v (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 (Set.range.{u2, 1} V (Fin n) (Fin.tail.{u2} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => V) v))))))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {n : Nat} {v : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> V}, Iff (LinearIndependent.{0, u1, u2} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) K V v (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (And (LinearIndependent.{0, u1, u2} (Fin n) K V (Fin.tail.{u2} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => V) v) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Not (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)) (v (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 (Set.range.{u2, 1} V (Fin n) (Fin.tail.{u2} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => V) v))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_fin_succ linearIndependent_fin_succₓ'. -/
 theorem linearIndependent_fin_succ {n} {v : Fin (n + 1) → V} :
     LinearIndependent K v ↔
@@ -1846,7 +1846,7 @@ theorem linearIndependent_fin_succ {n} {v : Fin (n + 1) → V} :
 lean 3 declaration is
   forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : DivisionRing.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_4 : Module.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {n : Nat} {v : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> V}, Iff (LinearIndependent.{0, u2, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) K V v (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (And (LinearIndependent.{0, u2, u1} (Fin n) K V (Fin.init.{u1} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => V) v) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Not (Membership.Mem.{u1, u1} V (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (SetLike.hasMem.{u1, u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) V (Submodule.setLike.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)) (v (Fin.last n)) (Submodule.span.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4 (Set.range.{u1, 1} V (Fin n) (Fin.init.{u1} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => V) v))))))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {n : Nat} {v : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> V}, Iff (LinearIndependent.{0, u1, u2} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) K V v (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (And (LinearIndependent.{0, u1, u2} (Fin n) K V (Fin.init.{u2} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => V) v) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Not (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)) (v (Fin.last n)) (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 (Set.range.{u2, 1} V (Fin n) (Fin.init.{u2} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => V) v))))))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {n : Nat} {v : (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> V}, Iff (LinearIndependent.{0, u1, u2} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) K V v (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (And (LinearIndependent.{0, u1, u2} (Fin n) K V (Fin.init.{u2} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => V) v) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Not (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)) (v (Fin.last n)) (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 (Set.range.{u2, 1} V (Fin n) (Fin.init.{u2} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => V) v))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_fin_succ' linearIndependent_fin_succ'ₓ'. -/
 theorem linearIndependent_fin_succ' {n} {v : Fin (n + 1) → V} :
     LinearIndependent K v ↔
@@ -1870,7 +1870,7 @@ theorem linearIndependent_fin2 {f : Fin 2 → V} :
 lean 3 declaration is
   forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : DivisionRing.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_4 : Module.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {s : Set.{u1} V} {t : Set.{u1} V}, (LinearIndependent.{u1, u2, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) K V ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (coeSubtype.{succ u1} V (fun (x : V) => Membership.Mem.{u1, u1} V (Set.{u1} V) (Set.hasMem.{u1} V) x s)))))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) -> (HasSubset.Subset.{u1} (Set.{u1} V) (Set.hasSubset.{u1} V) s t) -> (Exists.{succ u1} (Set.{u1} V) (fun (b : Set.{u1} V) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} V) (Set.hasSubset.{u1} V) b t) (fun (H : HasSubset.Subset.{u1} (Set.{u1} V) (Set.hasSubset.{u1} V) b t) => And (HasSubset.Subset.{u1} (Set.{u1} V) (Set.hasSubset.{u1} V) s b) (And (HasSubset.Subset.{u1} (Set.{u1} V) (Set.hasSubset.{u1} V) t ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Set.{u1} V) (HasLiftT.mk.{succ u1, succ u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Set.{u1} V) (CoeTCₓ.coe.{succ u1, succ u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Set.{u1} V) (SetLike.Set.hasCoeT.{u1, u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) V (Submodule.setLike.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)))) (Submodule.span.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4 b))) (LinearIndependent.{u1, u2, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) b) K V ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) b) V (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) b) V (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) b) V (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) b) V (coeSubtype.{succ u1} V (fun (x : V) => Membership.Mem.{u1, u1} V (Set.{u1} V) (Set.hasMem.{u1} V) x b)))))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)))))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {s : Set.{u2} V} {t : Set.{u2} V}, (LinearIndependent.{u2, u1, u2} (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s)) K V (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) -> (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) s t) -> (Exists.{succ u2} (Set.{u2} V) (fun (b : Set.{u2} V) => Exists.{0} (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) b t) (fun (H : HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) b t) => And (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) s b) (And (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) t (SetLike.coe.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 b))) (LinearIndependent.{u2, u1, u2} (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x b)) K V (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x b)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)))))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {s : Set.{u2} V} {t : Set.{u2} V}, (LinearIndependent.{u2, u1, u2} (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s)) K V (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) -> (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) s t) -> (Exists.{succ u2} (Set.{u2} V) (fun (b : Set.{u2} V) => Exists.{0} (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) b t) (fun (H : HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) b t) => And (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) s b) (And (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) t (SetLike.coe.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 b))) (LinearIndependent.{u2, u1, u2} (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x b)) K V (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x b)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)))))
 Case conversion may be inaccurate. Consider using '#align exists_linear_independent_extension exists_linearIndependent_extensionₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ⊆ » t) -/
 theorem exists_linearIndependent_extension (hs : LinearIndependent K (coe : s → V)) (hst : s ⊆ t) :
@@ -1945,7 +1945,7 @@ theorem LinearIndependent.subset_extend (hs : LinearIndependent K (fun x => x :
 lean 3 declaration is
   forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : DivisionRing.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_4 : Module.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {s : Set.{u1} V} {t : Set.{u1} V} (hs : LinearIndependent.{u1, u2, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) K V (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (coeSubtype.{succ u1} V (fun (x : V) => Membership.Mem.{u1, u1} V (Set.{u1} V) (Set.hasMem.{u1} V) x s))))) x) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (hst : HasSubset.Subset.{u1} (Set.{u1} V) (Set.hasSubset.{u1} V) s t), HasSubset.Subset.{u1} (Set.{u1} V) (Set.hasSubset.{u1} V) t ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Set.{u1} V) (HasLiftT.mk.{succ u1, succ u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Set.{u1} V) (CoeTCₓ.coe.{succ u1, succ u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Set.{u1} V) (SetLike.Set.hasCoeT.{u1, u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) V (Submodule.setLike.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)))) (Submodule.span.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4 (LinearIndependent.extend.{u1, u2} K V _inst_1 _inst_2 _inst_4 s t hs hst)))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {s : Set.{u2} V} {t : Set.{u2} V} (hs : LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} V s) K V (fun (x : Set.Elem.{u2} V s) => Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s) x) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (hst : HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) s t), HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) t (SetLike.coe.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 (LinearIndependent.extend.{u2, u1} K V _inst_1 _inst_2 _inst_4 s t hs hst)))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {s : Set.{u2} V} {t : Set.{u2} V} (hs : LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} V s) K V (fun (x : Set.Elem.{u2} V s) => Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s) x) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (hst : HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) s t), HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) t (SetLike.coe.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 (LinearIndependent.extend.{u2, u1} K V _inst_1 _inst_2 _inst_4 s t hs hst)))
 Case conversion may be inaccurate. Consider using '#align linear_independent.subset_span_extend LinearIndependent.subset_span_extendₓ'. -/
 theorem LinearIndependent.subset_span_extend (hs : LinearIndependent K (fun x => x : s → V))
     (hst : s ⊆ t) : t ⊆ span K (hs.extend hst) :=
@@ -1971,7 +1971,7 @@ variable {K V}
 lean 3 declaration is
   forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : DivisionRing.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_4 : Module.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {s : Set.{u1} V} {t : Finset.{u1} V}, (LinearIndependent.{u1, u2, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) K V (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (coeSubtype.{succ u1} V (fun (x : V) => Membership.Mem.{u1, u1} V (Set.{u1} V) (Set.hasMem.{u1} V) x s))))) x) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) -> (HasSubset.Subset.{u1} (Set.{u1} V) (Set.hasSubset.{u1} V) s ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Set.{u1} V) (HasLiftT.mk.{succ u1, succ u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Set.{u1} V) (CoeTCₓ.coe.{succ u1, succ u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Set.{u1} V) (SetLike.Set.hasCoeT.{u1, u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) V (Submodule.setLike.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)))) (Submodule.span.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} V) (Set.{u1} V) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} V) (Set.{u1} V) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} V) (Set.{u1} V) (Finset.Set.hasCoeT.{u1} V))) t)))) -> (Exists.{succ u1} (Finset.{u1} V) (fun (t' : Finset.{u1} V) => And (HasSubset.Subset.{u1} (Set.{u1} V) (Set.hasSubset.{u1} V) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} V) (Set.{u1} V) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} V) (Set.{u1} V) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} V) (Set.{u1} V) (Finset.Set.hasCoeT.{u1} V))) t') (Union.union.{u1} (Set.{u1} V) (Set.hasUnion.{u1} V) s ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} V) (Set.{u1} V) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} V) (Set.{u1} V) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} V) (Set.{u1} V) (Finset.Set.hasCoeT.{u1} V))) t))) (And (HasSubset.Subset.{u1} (Set.{u1} V) (Set.hasSubset.{u1} V) s ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} V) (Set.{u1} V) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} V) (Set.{u1} V) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} V) (Set.{u1} V) (Finset.Set.hasCoeT.{u1} V))) t')) (Eq.{1} Nat (Finset.card.{u1} V t') (Finset.card.{u1} V t)))))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {s : Set.{u2} V} {t : Finset.{u2} V}, (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} V s) K V (fun (x : Set.Elem.{u2} V s) => Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s) x) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) -> (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) s (SetLike.coe.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 (Finset.toSet.{u2} V t)))) -> (Exists.{succ u2} (Finset.{u2} V) (fun (t' : Finset.{u2} V) => And (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) (Finset.toSet.{u2} V t') (Union.union.{u2} (Set.{u2} V) (Set.instUnionSet.{u2} V) s (Finset.toSet.{u2} V t))) (And (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) s (Finset.toSet.{u2} V t')) (Eq.{1} Nat (Finset.card.{u2} V t') (Finset.card.{u2} V t)))))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {s : Set.{u2} V} {t : Finset.{u2} V}, (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} V s) K V (fun (x : Set.Elem.{u2} V s) => Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s) x) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) -> (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) s (SetLike.coe.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 (Finset.toSet.{u2} V t)))) -> (Exists.{succ u2} (Finset.{u2} V) (fun (t' : Finset.{u2} V) => And (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) (Finset.toSet.{u2} V t') (Union.union.{u2} (Set.{u2} V) (Set.instUnionSet.{u2} V) s (Finset.toSet.{u2} V t))) (And (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) s (Finset.toSet.{u2} V t')) (Eq.{1} Nat (Finset.card.{u2} V t') (Finset.card.{u2} V t)))))
 Case conversion may be inaccurate. Consider using '#align exists_of_linear_independent_of_finite_span exists_of_linearIndependent_of_finite_spanₓ'. -/
 -- TODO(Mario): rewrite?
 theorem exists_of_linearIndependent_of_finite_span {t : Finset V}
@@ -2040,7 +2040,7 @@ theorem exists_of_linearIndependent_of_finite_span {t : Finset V}
 lean 3 declaration is
   forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : DivisionRing.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_4 : Module.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {s : Set.{u1} V} {t : Set.{u1} V} (ht : Set.Finite.{u1} V t), (LinearIndependent.{u1, u2, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) K V (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (coeSubtype.{succ u1} V (fun (x : V) => Membership.Mem.{u1, u1} V (Set.{u1} V) (Set.hasMem.{u1} V) x s))))) x) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) -> (HasSubset.Subset.{u1} (Set.{u1} V) (Set.hasSubset.{u1} V) s ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Set.{u1} V) (HasLiftT.mk.{succ u1, succ u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Set.{u1} V) (CoeTCₓ.coe.{succ u1, succ u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Set.{u1} V) (SetLike.Set.hasCoeT.{u1, u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) V (Submodule.setLike.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)))) (Submodule.span.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4 t))) -> (Exists.{0} (Set.Finite.{u1} V s) (fun (h : Set.Finite.{u1} V s) => LE.le.{0} Nat Nat.hasLe (Finset.card.{u1} V (Set.Finite.toFinset.{u1} V s h)) (Finset.card.{u1} V (Set.Finite.toFinset.{u1} V t ht))))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {s : Set.{u2} V} {t : Set.{u2} V} (ht : Set.Finite.{u2} V t), (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} V s) K V (fun (x : Set.Elem.{u2} V s) => Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s) x) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) -> (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) s (SetLike.coe.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 t))) -> (Exists.{0} (Set.Finite.{u2} V s) (fun (h : Set.Finite.{u2} V s) => LE.le.{0} Nat instLENat (Finset.card.{u2} V (Set.Finite.toFinset.{u2} V s h)) (Finset.card.{u2} V (Set.Finite.toFinset.{u2} V t ht))))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {s : Set.{u2} V} {t : Set.{u2} V} (ht : Set.Finite.{u2} V t), (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} V s) K V (fun (x : Set.Elem.{u2} V s) => Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s) x) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) -> (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) s (SetLike.coe.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 t))) -> (Exists.{0} (Set.Finite.{u2} V s) (fun (h : Set.Finite.{u2} V s) => LE.le.{0} Nat instLENat (Finset.card.{u2} V (Set.Finite.toFinset.{u2} V s h)) (Finset.card.{u2} V (Set.Finite.toFinset.{u2} V t ht))))
 Case conversion may be inaccurate. Consider using '#align exists_finite_card_le_of_finite_of_linear_independent_of_span exists_finite_card_le_of_finite_of_linearIndependent_of_spanₓ'. -/
 theorem exists_finite_card_le_of_finite_of_linearIndependent_of_span (ht : t.Finite)
     (hs : LinearIndependent K (fun x => x : s → V)) (hst : s ⊆ span K t) :

bump to nightly-2023-03-17-00

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

c85864d4

Diff

@@ -167,8 +167,7 @@ theorem linearIndependent_iff'' :
   linearIndependent_iff'.trans
     ⟨fun H s g hg hv i => if his : i ∈ s then H s g hv i his else hg i his, fun H s g hg i hi =>
       by
-      convert
-        H s (fun j => if j ∈ s then g j else 0) (fun j hj => if_neg hj)
+      convert H s (fun j => if j ∈ s then g j else 0) (fun j hj => if_neg hj)
           (by simp_rw [ite_smul, zero_smul, Finset.sum_extend_by_zero, hg]) i
       exact (if_pos hi).symm⟩
 #align linear_independent_iff'' linearIndependent_iff''
@@ -208,7 +207,7 @@ theorem Fintype.linearIndependent_iff [Fintype ι] :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] [_inst_8 : Fintype.{u1} ι], Iff (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5) (Eq.{succ (max u1 u2)} (Submodule.{u2, max u1 u2} R (forall (i : ι), (fun (i : ι) => R) i) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i))) (LinearMap.ker.{u2, u2, max u1 u2, u3, max (max u1 u2) u3} R R (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) 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_inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.module.{u2, u2, 0, u2, u3} R R Nat ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.module.{u2, u2, 0, max u1 u2, u3} R R Nat (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) => (forall (i : ι), LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) -> (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (forall (i : ι), (fun (i : ι) => R) i) M (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5)) (LinearEquiv.hasCoeToFun.{0, 0, max u1 u2 u3, max (max u1 u2) u3} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (forall (i : ι), (fun (i : ι) => R) i) M (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, max u2 u3} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u1 u2, u3} R R (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u1, max u2 u3, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.module.{u2, u2, 0, u2, u3} R R Nat ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.module.{u2, u2, 0, max u1 u2, u3} R R Nat (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)) (LinearMap.lsum.{u2, u3, u1, u2, 0} R M ι _inst_1 (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) Nat _inst_2 _inst_5 _inst_8 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u1} ι a b)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5))) (fun (i : ι) => LinearMap.smulRight.{u2, u2, u3, u2} R ((fun (i : ι) => R) i) M ((fun (i : ι) => R) i) _inst_1 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) _inst_5 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_1 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (IsScalarTower.left.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2))) (Module.toMulActionWithZero.{u2, u3} R M _inst_1 _inst_2 _inst_5))) (LinearMap.id.{u2, u2} R ((fun (i : ι) => R) i) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) (v i)))) (Bot.bot.{max u1 u2} (Submodule.{u2, max u1 u2} R (forall (i : ι), (fun (i : ι) => R) i) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i))) (Submodule.hasBot.{u2, max u1 u2} R (forall (i : ι), (fun (i : ι) => R) i) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] [_inst_8 : Fintype.{u3} ι], Iff (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) (Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.ker.{u2, u2, max u3 u2, u1, max (max u3 u2) u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun 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(Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (_x : forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun 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(Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) _x) (SMulHomClass.toFunLike.{max (max u2 u3) u1, 0, max (max u2 u3) u1, max (max u2 u3) u1} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u1, 0, max (max u2 u3) u1, max (max u2 u3) u1} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (SemilinearMapClass.distribMulActionHomClass.{0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (LinearMap.lsum.{u2, u1, u3, u2, 0} R M ι _inst_1 (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) Nat _inst_2 _inst_5 _inst_8 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u3} ι a b)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (fun (i : ι) => LinearMap.smulRight.{u2, u2, u1, u2} R R M R _inst_1 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) _inst_5 (Semiring.toModule.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R _inst_1) _inst_5 (IsScalarTower.left.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (LinearMap.id.{u2, u2} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (v i)))) (Bot.bot.{max u3 u2} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (Submodule.instBotSubmodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] [_inst_8 : Fintype.{u3} ι], Iff (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) (Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.ker.{u2, u2, max u3 u2, u1, max (max u3 u2) u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (_x : forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) _x) (SMulHomClass.toFunLike.{max (max u2 u3) u1, 0, max (max u2 u3) u1, max (max u2 u3) u1} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u1, 0, max (max u2 u3) u1, max (max u2 u3) u1} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (SemilinearMapClass.distribMulActionHomClass.{0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (LinearMap.lsum.{u2, u1, u3, u2, 0} R M ι _inst_1 (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) Nat _inst_2 _inst_5 _inst_8 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u3} ι a b)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (fun (i : ι) => LinearMap.smulRight.{u2, u2, u1, u2} R R M R _inst_1 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) _inst_5 (Semiring.toModule.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R _inst_1) _inst_5 (IsScalarTower.left.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (LinearMap.id.{u2, u2} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (v i)))) (Bot.bot.{max u3 u2} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (Submodule.instBotSubmodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1442 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align fintype.linear_independent_iff' Fintype.linearIndependent_iff'ₓ'. -/
 /-- A finite family of vectors `v i` is linear independent iff the linear map that sends
 `c : ι → R` to `∑ i, c i • v i` has the trivial kernel. -/
@@ -791,7 +790,7 @@ theorem LinearIndependent.image {ι} {s : Set ι} {f : ι → M}
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {G : Type.{u4}} [hG : Group.{u4} G] [_inst_8 : DistribMulAction.{u4, u2} G R (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (NonAssocRing.toAddGroupWithOne.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))] [_inst_9 : DistribMulAction.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))] [_inst_10 : IsScalarTower.{u4, u2, u3} G R M (SMulZeroClass.toHasSmul.{u4, u2} G R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (NonAssocRing.toAddGroupWithOne.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (DistribSMul.toSmulZeroClass.{u4, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (NonAssocRing.toAddGroupWithOne.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{u4, u2} G R (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (NonAssocRing.toAddGroupWithOne.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) _inst_8))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)))) (SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u4, u2, u3} G R M (SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u1, u2, u3} ι R M (SMul.smul.{max u1 u4, max u1 u3} (ι -> G) (ι -> M) (Pi.smul'.{u1, u4, u3} ι (fun (ᾰ : ι) => G) (fun (ᾰ : ι) => M) (fun (i : ι) => SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9)))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)
 but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {G : Type.{u3}} [hG : Group.{u3} G] [_inst_8 : DistribMulAction.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))] [_inst_9 : DistribMulAction.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))] [_inst_10 : IsScalarTower.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u2} G R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (DistribSMul.toSMulZeroClass.{u3, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))) (DistribMulAction.toDistribSMul.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1))) _inst_8))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u4, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u4, u2, u1} ι R M (HSMul.hSMul.{max u4 u3, max u4 u1, max u4 u1} (ι -> G) (ι -> M) (ι -> M) (instHSMul.{max u4 u3, max u4 u1} (ι -> G) (ι -> M) (Pi.smul'.{u4, u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6582 : ι) => G) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6576 : ι) => M) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
+  forall {ι : Type.{u4}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {G : Type.{u3}} [hG : Group.{u3} G] [_inst_8 : DistribMulAction.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))] [_inst_9 : DistribMulAction.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))] [_inst_10 : IsScalarTower.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u2} G R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (DistribSMul.toSMulZeroClass.{u3, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))) (DistribMulAction.toDistribSMul.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1))) _inst_8))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u4, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u4, u2, u1} ι R M (HSMul.hSMul.{max u4 u3, max u4 u1, max u4 u1} (ι -> G) (ι -> M) (ι -> M) (instHSMul.{max u4 u3, max u4 u1} (ι -> G) (ι -> M) (Pi.smul'.{u4, u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6835 : ι) => G) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6829 : ι) => M) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent.group_smul LinearIndependent.group_smulₓ'. -/
 theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulAction G R]
     [DistribMulAction G M] [IsScalarTower G R M] [SMulCommClass G R M] {v : ι → M}
@@ -812,7 +811,7 @@ theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulActi
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {v : ι -> M}, (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall (w : ι -> (Units.{u2} R (Ring.toMonoid.{u2} R _inst_1))), LinearIndependent.{u1, u2, u3} ι R M (SMul.smul.{max u1 u2, max u1 u3} (ι -> (Units.{u2} R (Ring.toMonoid.{u2} R _inst_1))) (ι -> M) (Pi.smul'.{u1, u2, u3} ι (fun (ᾰ : ι) => Units.{u2} R (Ring.toMonoid.{u2} R _inst_1)) (fun (ᾰ : ι) => M) (fun (i : ι) => Units.hasSmul.{u2, u3} R M (Ring.toMonoid.{u2} R _inst_1) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {v : ι -> M}, (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))), LinearIndependent.{u3, u2, u1} ι R M (HSMul.hSMul.{max u3 u2, max u3 u1, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (ι -> M) (instHSMul.{max u3 u2, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6812 : ι) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6806 : ι) => M) (fun (i : ι) => Units.instSMulUnits.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {v : ι -> M}, (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))), LinearIndependent.{u3, u2, u1} ι R M (HSMul.hSMul.{max u3 u2, max u3 u1, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (ι -> M) (instHSMul.{max u3 u2, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.7065 : ι) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.7059 : ι) => M) (fun (i : ι) => Units.instSMulUnits.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent.units_smul LinearIndependent.units_smulₓ'. -/
 -- This lemma cannot be proved with `linear_independent.group_smul` since the action of
 -- `Rˣ` on `R` is not commutative.
@@ -1464,7 +1463,7 @@ theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv :
 lean 3 declaration is
   forall (G : Type.{u1}) [_inst_8 : Monoid.{u1} G] (L : Type.{u2}) [_inst_9 : CommRing.{u2} L] [_inst_10 : NoZeroDivisors.{u2} L (Distrib.toHasMul.{u2} L (Ring.toDistrib.{u2} L (CommRing.toRing.{u2} L _inst_9))) (MulZeroClass.toHasZero.{u2} L (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9))))))], LinearIndependent.{max u2 u1, u2, max u1 u2} (MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) => coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) (fun (_x : MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) => G -> L) (MonoidHom.hasCoeToFun.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) f) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9)) (Pi.addCommMonoid.{u1, u2} G (fun (ᾰ : G) => L) (fun (i : G) => AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) (Pi.Function.module.{u1, u2, u2} G L L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9)) (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9))))) (Semiring.toModule.{u2} L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9))))
 but is expected to have type
-  forall (G : Type.{u2}) [_inst_8 : Monoid.{u2} G] (L : Type.{u1}) [_inst_9 : CommRing.{u1} L] [_inst_10 : NoZeroDivisors.{u1} L (NonUnitalNonAssocRing.toMul.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9)))) (CommMonoidWithZero.toZero.{u1} L (CommSemiring.toCommMonoidWithZero.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))], LinearIndependent.{max u2 u1, u1, max u2 u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => L) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G _inst_8)) (MulOneClass.toMul.{u1} L (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (MonoidHom.monoidHomClass.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))))) f) (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (Pi.addCommMonoid.{u2, u1} G (fun (ᾰ : G) => L) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9)))))) (Pi.module.{u2, u1, u1} G (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.14614 : G) => L) L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9))))) (fun (i : G) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))
+  forall (G : Type.{u2}) [_inst_8 : Monoid.{u2} G] (L : Type.{u1}) [_inst_9 : CommRing.{u1} L] [_inst_10 : NoZeroDivisors.{u1} L (NonUnitalNonAssocRing.toMul.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9)))) (CommMonoidWithZero.toZero.{u1} L (CommSemiring.toCommMonoidWithZero.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))], LinearIndependent.{max u2 u1, u1, max u2 u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => L) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G _inst_8)) (MulOneClass.toMul.{u1} L (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (MonoidHom.monoidHomClass.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))))) f) (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (Pi.addCommMonoid.{u2, u1} G (fun (ᾰ : G) => L) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9)))))) (Pi.module.{u2, u1, u1} G (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.14954 : G) => L) L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9))))) (fun (i : G) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))
 Case conversion may be inaccurate. Consider using '#align linear_independent_monoid_hom linearIndependent_monoidHomₓ'. -/
 -- See, for example, Keith Conrad's note
 --  <https://kconrad.math.uconn.edu/blurbs/galoistheory/linearchar.pdf>

bump to nightly-2023-03-11-22

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

a8ee822f

Diff

@@ -116,7 +116,7 @@ variable {R} {v}
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2], Iff (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), (Eq.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u3, u2} ι M R _inst_1 _inst_2 _inst_5 v) l) (OfNat.ofNat.{u3} M 0 (OfNat.mk.{u3} M 0 (Zero.zero.{u3} M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2))))))) -> (Eq.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) l (OfNat.ofNat.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) 0 (OfNat.mk.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) 0 (Zero.zero.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Finsupp.zero.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.zero.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.zero.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_iff linearIndependent_iffₓ'. -/
 theorem linearIndependent_iff : LinearIndependent R v ↔ ∀ l, Finsupp.total ι M R v l = 0 → l = 0 :=
   by simp [LinearIndependent, LinearMap.ker_eq_bot']
@@ -208,7 +208,7 @@ theorem Fintype.linearIndependent_iff [Fintype ι] :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] [_inst_8 : Fintype.{u1} ι], Iff (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5) (Eq.{succ (max u1 u2)} (Submodule.{u2, max u1 u2} R (forall (i : ι), (fun (i : ι) => R) i) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i))) (LinearMap.ker.{u2, u2, max u1 u2, u3, max (max u1 u2) u3} R R (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) 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(Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (coeFn.{max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3)), max (succ (max u1 u2 u3)) (succ (max (max u1 u2) u3))} (LinearEquiv.{0, 0, max u1 u2 u3, max (max u1 u2) u3} Nat Nat Nat.semiring Nat.semiring 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_inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.module.{u2, u2, 0, u2, u3} R R Nat ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.module.{u2, u2, 0, max u1 u2, u3} R R Nat (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) => (forall (i : ι), LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) -> (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (forall (i : ι), (fun (i : ι) => R) i) M (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5)) (LinearEquiv.hasCoeToFun.{0, 0, max u1 u2 u3, max (max u1 u2) u3} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (forall (i : ι), (fun (i : ι) => R) i) M (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, max u2 u3} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u1 u2, u3} R R (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u1, max u2 u3, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.module.{u2, u2, 0, u2, u3} R R Nat ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.module.{u2, u2, 0, max u1 u2, u3} R R Nat (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)) (LinearMap.lsum.{u2, u3, u1, u2, 0} R M ι _inst_1 (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) Nat _inst_2 _inst_5 _inst_8 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u1} ι a b)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5))) (fun (i : ι) => LinearMap.smulRight.{u2, u2, u3, u2} R ((fun (i : ι) => R) i) M ((fun (i : ι) => R) i) _inst_1 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) _inst_5 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_1 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (IsScalarTower.left.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2))) (Module.toMulActionWithZero.{u2, u3} R M _inst_1 _inst_2 _inst_5))) (LinearMap.id.{u2, u2} R ((fun (i : ι) => R) i) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) (v i)))) (Bot.bot.{max u1 u2} (Submodule.{u2, max u1 u2} R (forall (i : ι), (fun (i : ι) => R) i) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i))) (Submodule.hasBot.{u2, max u1 u2} R (forall (i : ι), (fun (i : ι) => R) i) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] [_inst_8 : Fintype.{u3} ι], Iff (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) (Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.ker.{u2, u2, max u3 u2, u1, max (max u3 u2) u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun 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(x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u1, 0, max (max u2 u3) u1, max (max u2 u3) u1} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (SemilinearMapClass.distribMulActionHomClass.{0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (LinearMap.lsum.{u2, u1, u3, u2, 0} R M ι _inst_1 (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) Nat _inst_2 _inst_5 _inst_8 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u3} ι a b)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (fun (i : ι) => LinearMap.smulRight.{u2, u2, u1, u2} R R M R _inst_1 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) _inst_5 (Semiring.toModule.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R _inst_1) _inst_5 (IsScalarTower.left.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (LinearMap.id.{u2, u2} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (v i)))) (Bot.bot.{max u3 u2} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (Submodule.instBotSubmodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] [_inst_8 : Fintype.{u3} ι], Iff (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) (Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.ker.{u2, u2, max u3 u2, u1, max (max u3 u2) u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun 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(x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (max (succ u2) (succ u3)) (succ u1), max (max (succ u2) (succ u3)) (succ u1)} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun 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i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (_x : forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) _x) (SMulHomClass.toFunLike.{max (max u2 u3) u1, 0, max (max u2 u3) u1, max (max u2 u3) u1} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u1, 0, max (max u2 u3) u1, max (max u2 u3) u1} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (SemilinearMapClass.distribMulActionHomClass.{0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (LinearMap.lsum.{u2, u1, u3, u2, 0} R M ι _inst_1 (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) Nat _inst_2 _inst_5 _inst_8 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u3} ι a b)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (fun (i : ι) => LinearMap.smulRight.{u2, u2, u1, u2} R R M R _inst_1 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) _inst_5 (Semiring.toModule.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R _inst_1) _inst_5 (IsScalarTower.left.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (LinearMap.id.{u2, u2} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (v i)))) (Bot.bot.{max u3 u2} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (Submodule.instBotSubmodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1401 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align fintype.linear_independent_iff' Fintype.linearIndependent_iff'ₓ'. -/
 /-- A finite family of vectors `v i` is linear independent iff the linear map that sends
 `c : ι → R` to `∑ i, c i • v i` has the trivial kernel. -/
@@ -290,7 +290,7 @@ theorem LinearIndependent.coe_range (i : LinearIndependent R v) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {M' : Type.{u4}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u4} M'] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] [_inst_6 : Module.{u2, u4} R M' _inst_1 _inst_3], (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5) -> (forall {f : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6}, (Disjoint.{u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (SetLike.partialOrder.{u3, u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u2, u3} R M _inst_1 _inst_2 _inst_5)) (Submodule.orderBot.{u2, u3} R M _inst_1 _inst_2 _inst_5) (Submodule.span.{u2, u3} R M _inst_1 _inst_2 _inst_5 (Set.range.{u3, succ u1} M ι v)) (LinearMap.ker.{u2, u2, u3, u4, max u3 u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f)) -> (LinearIndependent.{u1, u2, u4} ι R M' (Function.comp.{succ u1, succ u3, succ u4} ι M M' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
 but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3], (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5) -> (forall {f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6}, (Disjoint.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.completeLattice.{u3, u2} R M _inst_1 _inst_2 _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.span.{u3, u2} R M _inst_1 _inst_2 _inst_5 (Set.range.{u2, succ u4} M ι v)) (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
+  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3], (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5) -> (forall {f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6}, (Disjoint.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.completeLattice.{u3, u2} R M _inst_1 _inst_2 _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.span.{u3, u2} R M _inst_1 _inst_2 _inst_5 (Set.range.{u2, succ u4} M ι v)) (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
 Case conversion may be inaccurate. Consider using '#align linear_independent.map LinearIndependent.mapₓ'. -/
 /-- If `v` is a linearly independent family of vectors and the kernel of a linear map `f` is
 disjoint with the submodule spanned by the vectors of `v`, then `f ∘ v` is a linearly independent
@@ -313,7 +313,7 @@ theorem LinearIndependent.map (hv : LinearIndependent R v) {f : M →ₗ[R] M'}
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {M' : Type.{u4}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u4} M'] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] [_inst_6 : Module.{u2, u4} R M' _inst_1 _inst_3], (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5) -> (forall (f : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (Eq.{succ u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (LinearMap.ker.{u2, u2, u3, u4, max u3 u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (Bot.bot.{u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (Submodule.hasBot.{u2, u3} R M _inst_1 _inst_2 _inst_5))) -> (LinearIndependent.{u1, u2, u4} ι R M' (Function.comp.{succ u1, succ u3, succ u4} ι M M' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
 but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3], (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5) -> (forall (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) (Bot.bot.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.instBotSubmodule.{u3, u2} R M _inst_1 _inst_2 _inst_5))) -> (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
+  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3], (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5) -> (forall (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) (Bot.bot.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.instBotSubmodule.{u3, u2} R M _inst_1 _inst_2 _inst_5))) -> (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6))
 Case conversion may be inaccurate. Consider using '#align linear_independent.map' LinearIndependent.map'ₓ'. -/
 /-- An injective linear map sends linearly independent families of vectors to linearly independent
 families of vectors. See also `linear_independent.map` for a more general statement. -/
@@ -326,7 +326,7 @@ theorem LinearIndependent.map' (hv : LinearIndependent R v) (f : M →ₗ[R] M')
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {M' : Type.{u4}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u4} M'] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] [_inst_6 : Module.{u2, u4} R M' _inst_1 _inst_3] (f : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (LinearIndependent.{u1, u2, u4} ι R M' (Function.comp.{succ u1, succ u3, succ u4} ι M M' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6) -> (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5)
 but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6) -> (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5)
+  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6) -> (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent.of_comp LinearIndependent.of_compₓ'. -/
 /-- If the image of a family of vectors under a linear map is linearly independent, then so is
 the original family. -/
@@ -342,7 +342,7 @@ theorem LinearIndependent.of_comp (f : M →ₗ[R] M') (hfv : LinearIndependent
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {M' : Type.{u4}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u4} M'] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] [_inst_6 : Module.{u2, u4} R M' _inst_1 _inst_3] (f : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (Eq.{succ u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (LinearMap.ker.{u2, u2, u3, u4, max u3 u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.semilinearMapClass.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) (Bot.bot.{u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (Submodule.hasBot.{u2, u3} R M _inst_1 _inst_2 _inst_5))) -> (Iff (LinearIndependent.{u1, u2, u4} ι R M' (Function.comp.{succ u1, succ u3, succ u4} ι M M' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (fun (_x : LinearMap.{u2, u2, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u2, u2, u3, u4} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6) (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5))
 but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) (Bot.bot.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.instBotSubmodule.{u3, u2} R M _inst_1 _inst_2 _inst_5))) -> (Iff (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6) (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5))
+  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} M'] [_inst_5 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : Module.{u3, u1} R M' _inst_1 _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6), (Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) (Bot.bot.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (Submodule.instBotSubmodule.{u3, u2} R M _inst_1 _inst_2 _inst_5))) -> (Iff (LinearIndependent.{u4, u3, u1} ι R M' (Function.comp.{succ u4, succ u2, succ u1} ι M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M M' _inst_2 _inst_3 _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' _inst_1 _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) v) _inst_1 _inst_3 _inst_6) (LinearIndependent.{u4, u3, u2} ι R M v _inst_1 _inst_2 _inst_5))
 Case conversion may be inaccurate. Consider using '#align linear_map.linear_independent_iff LinearMap.linearIndependent_iffₓ'. -/
 /-- If `f` is an injective linear map, then the family `f ∘ v` is linearly independent
 if and only if the family `v` is linearly independent. -/
@@ -366,7 +366,7 @@ theorem linearIndependent_of_subsingleton [Subsingleton R] : LinearIndependent R
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u4}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_5 : Module.{u3, u4} R M _inst_1 _inst_2] (e : Equiv.{succ u1, succ u2} ι ι') {f : ι' -> M}, Iff (LinearIndependent.{u1, u3, u4} ι R M (Function.comp.{succ u1, succ u2, succ u4} ι ι' M f (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} ι ι') (fun (_x : Equiv.{succ u1, succ u2} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{succ u1, succ u2} ι ι') e)) _inst_1 _inst_2 _inst_5) (LinearIndependent.{u2, u3, u4} ι' R M f _inst_1 _inst_2 _inst_5)
 but is expected to have type
-  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] (e : Equiv.{succ u4, succ u3} ι ι') {f : ι' -> M}, Iff (LinearIndependent.{u4, u2, u1} ι R M (Function.comp.{succ u4, succ u3, succ u1} ι ι' M f (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} ι ι') e)) _inst_1 _inst_2 _inst_5) (LinearIndependent.{u3, u2, u1} ι' R M f _inst_1 _inst_2 _inst_5)
+  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] (e : Equiv.{succ u4, succ u3} ι ι') {f : ι' -> M}, Iff (LinearIndependent.{u4, u2, u1} ι R M (Function.comp.{succ u4, succ u3, succ u1} ι ι' M f (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} ι ι') e)) _inst_1 _inst_2 _inst_5) (LinearIndependent.{u3, u2, u1} ι' R M f _inst_1 _inst_2 _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent_equiv linearIndependent_equivₓ'. -/
 theorem linearIndependent_equiv (e : ι ≃ ι') {f : ι' → M} :
     LinearIndependent R (f ∘ e) ↔ LinearIndependent R f :=
@@ -378,7 +378,7 @@ theorem linearIndependent_equiv (e : ι ≃ ι') {f : ι' → M} :
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u4}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_5 : Module.{u3, u4} R M _inst_1 _inst_2] (e : Equiv.{succ u1, succ u2} ι ι') {f : ι' -> M} {g : ι -> M}, (Eq.{max (succ u1) (succ u4)} (ι -> M) (Function.comp.{succ u1, succ u2, succ u4} ι ι' M f (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} ι ι') (fun (_x : Equiv.{succ u1, succ u2} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{succ u1, succ u2} ι ι') e)) g) -> (Iff (LinearIndependent.{u1, u3, u4} ι R M g _inst_1 _inst_2 _inst_5) (LinearIndependent.{u2, u3, u4} ι' R M f _inst_1 _inst_2 _inst_5))
 but is expected to have type
-  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] (e : Equiv.{succ u4, succ u3} ι ι') {f : ι' -> M} {g : ι -> M}, (Eq.{max (succ u4) (succ u2)} (ι -> M) (Function.comp.{succ u4, succ u3, succ u2} ι ι' M f (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} ι ι') e)) g) -> (Iff (LinearIndependent.{u4, u1, u2} ι R M g _inst_1 _inst_2 _inst_5) (LinearIndependent.{u3, u1, u2} ι' R M f _inst_1 _inst_2 _inst_5))
+  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] (e : Equiv.{succ u4, succ u3} ι ι') {f : ι' -> M} {g : ι -> M}, (Eq.{max (succ u4) (succ u2)} (ι -> M) (Function.comp.{succ u4, succ u3, succ u2} ι ι' M f (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} ι ι') e)) g) -> (Iff (LinearIndependent.{u4, u1, u2} ι R M g _inst_1 _inst_2 _inst_5) (LinearIndependent.{u3, u1, u2} ι' R M f _inst_1 _inst_2 _inst_5))
 Case conversion may be inaccurate. Consider using '#align linear_independent_equiv' linearIndependent_equiv'ₓ'. -/
 theorem linearIndependent_equiv' (e : ι ≃ ι') {f : ι' → M} {g : ι → M} (h : f ∘ e = g) :
     LinearIndependent R g ↔ LinearIndependent R f :=
@@ -508,7 +508,7 @@ section Subtype
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] {s : Set.{u1} ι}, Iff (LinearIndependent.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) R M (Function.comp.{succ u1, succ u1, succ u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι M v ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeSubtype.{succ u1} ι (fun (x : ι) => Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) x s))))))) _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), (Membership.Mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Submodule.setLike.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) l (Finsupp.supported.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s)) -> (Eq.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R 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 but is expected to have type
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_inst_1))) => M) l) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) l (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R 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+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, Iff (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))), (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) l (Finsupp.supported.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R 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(MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) l (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (Finsupp.zero.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_comp_subtype linearIndependent_comp_subtypeₓ'. -/
 theorem linearIndependent_comp_subtype {s : Set ι} :
     LinearIndependent R (v ∘ coe : s → M) ↔
@@ -533,7 +533,7 @@ theorem linearIndependent_comp_subtype {s : Set ι} :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] {s : Set.{u1} ι}, Iff (Not (LinearIndependent.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) R M (Function.comp.{succ u1, succ u1, succ u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι M v ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeSubtype.{succ u1} ι (fun (x : ι) => Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) x s))))))) _inst_1 _inst_2 _inst_5)) (Exists.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (fun (f : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) => And (Membership.Mem.{max u1 u2, max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Submodule.setLike.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) f (Finsupp.supported.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s)) (And (Eq.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, Iff (Not (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5)) (Exists.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (f : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => And (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R 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+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, Iff (Not (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5)) (Exists.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (f : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => And (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R 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 Case conversion may be inaccurate. Consider using '#align linear_dependent_comp_subtype' linearDependent_comp_subtype'ₓ'. -/
 theorem linearDependent_comp_subtype' {s : Set ι} :
     ¬LinearIndependent R (v ∘ coe : s → M) ↔
@@ -558,7 +558,7 @@ theorem linearDependent_comp_subtype {s : Set ι} :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M 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 but is expected to have type
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.instSetLikeSubmodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_2 _inst_5 (id.{succ u2} M)) l) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u1) (succ u2)} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) l (OfNat.ofNat.{max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) 0 (Zero.toOfNat0.{max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Finsupp.zero.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M s) R M (fun (x : Set.Elem.{u2} M s) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) x) _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))), (Membership.mem.{max u1 u2, max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.instSetLikeSubmodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_2 _inst_5 (id.{succ u2} M)) l) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u1) (succ u2)} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) l (OfNat.ofNat.{max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) 0 (Zero.toOfNat0.{max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Finsupp.zero.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_subtype linearIndependent_subtypeₓ'. -/
 theorem linearIndependent_subtype {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
@@ -700,7 +700,7 @@ variable {a b : R} {x y : M}
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], Iff (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Function.Injective.{max (succ u1) (succ u2), succ u3} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u1, u3, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 v)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], Iff (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Function.Injective.{max (succ u3) (succ u2), succ u1} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v)))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], Iff (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Function.Injective.{max (succ u3) (succ u2), succ u1} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v)))
 Case conversion may be inaccurate. Consider using '#align linear_independent_iff_injective_total linearIndependent_iff_injective_totalₓ'. -/
 theorem linearIndependent_iff_injective_total :
     LinearIndependent R v ↔ Function.Injective (Finsupp.total ι M R v) :=
@@ -712,7 +712,7 @@ theorem linearIndependent_iff_injective_total :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (Function.Injective.{max (succ u1) (succ u2), succ u3} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u1, u3, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 v)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (Function.Injective.{max (succ u3) (succ u2), succ u1} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v)))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (Function.Injective.{max (succ u3) (succ u2), succ u1} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v)))
 Case conversion may be inaccurate. Consider using '#align linear_independent.injective_total LinearIndependent.injective_totalₓ'. -/
 alias linearIndependent_iff_injective_total ↔ LinearIndependent.injective_total _
 #align linear_independent.injective_total LinearIndependent.injective_total
@@ -791,7 +791,7 @@ theorem LinearIndependent.image {ι} {s : Set ι} {f : ι → M}
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {G : Type.{u4}} [hG : Group.{u4} G] [_inst_8 : DistribMulAction.{u4, u2} G R (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (NonAssocRing.toAddGroupWithOne.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))] [_inst_9 : DistribMulAction.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))] [_inst_10 : IsScalarTower.{u4, u2, u3} G R M (SMulZeroClass.toHasSmul.{u4, u2} G R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (NonAssocRing.toAddGroupWithOne.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (DistribSMul.toSmulZeroClass.{u4, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (NonAssocRing.toAddGroupWithOne.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{u4, u2} G R (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (NonAssocRing.toAddGroupWithOne.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) _inst_8))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)))) (SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u4, u2, u3} G R M (SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u1, u2, u3} ι R M (SMul.smul.{max u1 u4, max u1 u3} (ι -> G) (ι -> M) (Pi.smul'.{u1, u4, u3} ι (fun (ᾰ : ι) => G) (fun (ᾰ : ι) => M) (fun (i : ι) => SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9)))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)
 but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {G : Type.{u3}} [hG : Group.{u3} G] [_inst_8 : DistribMulAction.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))] [_inst_9 : DistribMulAction.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))] [_inst_10 : IsScalarTower.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u2} G R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (DistribSMul.toSMulZeroClass.{u3, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))) (DistribMulAction.toDistribSMul.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1))) _inst_8))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u4, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u4, u2, u1} ι R M (HSMul.hSMul.{max u4 u3, max u4 u1, max u4 u1} (ι -> G) (ι -> M) (ι -> M) (instHSMul.{max u4 u3, max u4 u1} (ι -> G) (ι -> M) (Pi.smul'.{u4, u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6561 : ι) => G) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6555 : ι) => M) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
+  forall {ι : Type.{u4}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {G : Type.{u3}} [hG : Group.{u3} G] [_inst_8 : DistribMulAction.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))] [_inst_9 : DistribMulAction.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))] [_inst_10 : IsScalarTower.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u2} G R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (DistribSMul.toSMulZeroClass.{u3, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))) (DistribMulAction.toDistribSMul.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1))) _inst_8))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u4, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u4, u2, u1} ι R M (HSMul.hSMul.{max u4 u3, max u4 u1, max u4 u1} (ι -> G) (ι -> M) (ι -> M) (instHSMul.{max u4 u3, max u4 u1} (ι -> G) (ι -> M) (Pi.smul'.{u4, u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6582 : ι) => G) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6576 : ι) => M) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent.group_smul LinearIndependent.group_smulₓ'. -/
 theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulAction G R]
     [DistribMulAction G M] [IsScalarTower G R M] [SMulCommClass G R M] {v : ι → M}
@@ -812,7 +812,7 @@ theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulActi
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {v : ι -> M}, (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall (w : ι -> (Units.{u2} R (Ring.toMonoid.{u2} R _inst_1))), LinearIndependent.{u1, u2, u3} ι R M (SMul.smul.{max u1 u2, max u1 u3} (ι -> (Units.{u2} R (Ring.toMonoid.{u2} R _inst_1))) (ι -> M) (Pi.smul'.{u1, u2, u3} ι (fun (ᾰ : ι) => Units.{u2} R (Ring.toMonoid.{u2} R _inst_1)) (fun (ᾰ : ι) => M) (fun (i : ι) => Units.hasSmul.{u2, u3} R M (Ring.toMonoid.{u2} R _inst_1) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {v : ι -> M}, (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))), LinearIndependent.{u3, u2, u1} ι R M (HSMul.hSMul.{max u3 u2, max u3 u1, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (ι -> M) (instHSMul.{max u3 u2, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6791 : ι) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6785 : ι) => M) (fun (i : ι) => Units.instSMulUnits.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {v : ι -> M}, (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))), LinearIndependent.{u3, u2, u1} ι R M (HSMul.hSMul.{max u3 u2, max u3 u1, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (ι -> M) (instHSMul.{max u3 u2, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6812 : ι) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6806 : ι) => M) (fun (i : ι) => Units.instSMulUnits.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent.units_smul LinearIndependent.units_smulₓ'. -/
 -- This lemma cannot be proved with `linear_independent.group_smul` since the action of
 -- `Rˣ` on `R` is not commutative.
@@ -945,7 +945,7 @@ theorem LinearIndependent.not_mem_span_image [Nontrivial R] (hv : LinearIndepend
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_8 : Nontrivial.{u2} R], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall {x : ι} (f : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))), (Not (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) x (Finsupp.support.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) f))) -> (Ne.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u1, u3, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 v) f) (v x)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Nontrivial.{u2} R], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall {x : ι} (f : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))), (Not (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) x (Finsupp.support.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) f))) -> (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) f) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v) f) (v x)))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Nontrivial.{u2} R], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall {x : ι} (f : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))), (Not (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) x (Finsupp.support.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) f))) -> (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) f) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v) f) (v x)))
 Case conversion may be inaccurate. Consider using '#align linear_independent.total_ne_of_not_mem_support LinearIndependent.total_ne_of_not_mem_supportₓ'. -/
 theorem LinearIndependent.total_ne_of_not_mem_support [Nontrivial R] (hv : LinearIndependent R v)
     {x : ι} (f : ι →₀ R) (h : x ∉ f.support) : Finsupp.total ι M R v f ≠ v x :=
@@ -1136,7 +1136,7 @@ def LinearIndependent.repr (hv : LinearIndependent R v) : span R (range v) →
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))), Eq.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ 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(Ring.toSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u1, u3, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 v) (coeFn.{max (succ u3) (succ (max u1 u2)), max (succ u3) (succ (max u1 u2))} (LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) 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 but is expected to have type
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+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))), Eq.{succ u2} 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 Case conversion may be inaccurate. Consider using '#align linear_independent.total_repr LinearIndependent.total_reprₓ'. -/
 @[simp]
 theorem LinearIndependent.total_repr (x) : Finsupp.total ι M R v (hv.repr x) = x :=
@@ -1178,7 +1178,7 @@ theorem LinearIndependent.repr_range : hv.repr.range = ⊤ := by
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) {l : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))} {x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq LinearIndependent.repr_eqₓ'. -/
 theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M R v l = ↑x) :
     hv.repr x = l :=
@@ -1200,7 +1200,7 @@ theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (i : ι) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))), (Eq.{succ u3} M ((fun (a : Type.{u3}) (b : 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 but is expected to have type
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(instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv) x) (Finsupp.single.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) i (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (i : ι) (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))), 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succ u3} M ι v)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) 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(instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv) x) (Finsupp.single.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) i (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq_single LinearIndependent.repr_eq_singleₓ'. -/
 theorem LinearIndependent.repr_eq_single (i) (x) (hx : ↑x = v i) : hv.repr x = Finsupp.single i 1 :=
   by
@@ -1212,7 +1212,7 @@ theorem LinearIndependent.repr_eq_single (i) (x) (hx : ↑x = v i) : hv.repr x =
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) [_inst_8 : Nontrivial.{u2} R] (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))), Eq.{max (succ u3) 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ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) -> (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R 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(NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv) x))
 but is expected to have type
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succ u3} M ι v)))) => Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R 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R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv) x))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) [_inst_8 : Nontrivial.{u2} R] (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ 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succ u3} M ι v)))) => Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv) x))
 Case conversion may be inaccurate. Consider using '#align linear_independent.span_repr_eq LinearIndependent.span_repr_eqₓ'. -/
 theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
     Span.repr R (Set.range v) x = (hv.repr x).equivMapDomain (Equiv.ofInjective _ hv.Injective) :=
@@ -1419,7 +1419,7 @@ open LinearMap
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {M' : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_6 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3)] {s : Set.{u2} M} {f : LinearMap.{u1, u1, u2, u3} 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))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6}, (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => 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(Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) s)) M' (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M') Type.{u3} (Set.hasCoeToSort.{u3} M') (Set.image.{u2, u3} M M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} 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))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} 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))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) 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(AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) s)))))) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_3) _inst_6)
 but is expected to have type
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(Disjoint.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 s) (LinearMap.ker.{u2, u2, u3, u1, max u3 u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (LinearIndependent.{u1, u2, u1} (Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) R M' (fun (x : Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) => Subtype.val.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Set.{u1} M') (Set.instMembershipSet.{u1} M') x (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M') a) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_6)
+  forall {R : Type.{u2}} {M : Type.{u3}} {M' : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_6 : Module.{u2, u1} R M' (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)] {s : Set.{u3} M} {f : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6}, (LinearIndependent.{u3, u2, u3} (Set.Elem.{u3} M s) R M (fun (x : Set.Elem.{u3} M s) => Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x s) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (Disjoint.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 s) (LinearMap.ker.{u2, u2, u3, u1, max u3 u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (LinearIndependent.{u1, u2, u1} (Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) R M' (fun (x : Set.Elem.{u1} M' (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) => Subtype.val.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Set.{u1} M') (Set.instMembershipSet.{u1} M') x (Set.image.{u3, u1} M M' (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') a) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R M M' (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) s)) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_6)
 Case conversion may be inaccurate. Consider using '#align linear_independent.image_subtype LinearIndependent.image_subtypeₓ'. -/
 theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
     (hs : LinearIndependent R (fun x => x : s → M)) (hf_inj : Disjoint (span R s) f.ker) :
@@ -1434,7 +1434,7 @@ theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
 lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u2} M' _inst_3)) _inst_6 (Prod.module.{u1, u3, u2} R M M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.inr.{u1, u3, u2} R M M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_3) _inst_5 _inst_6)) t))) x) (Ring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u3, u2} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_3)) (Prod.module.{u1, u3, u2} R M M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_3) _inst_5 _inst_6))
 Case conversion may be inaccurate. Consider using '#align linear_independent.inl_union_inr LinearIndependent.inl_union_inrₓ'. -/
 theorem LinearIndependent.inl_union_inr {s : Set M} {t : Set M'}
     (hs : LinearIndependent R (fun x => x : s → M))
@@ -1450,7 +1450,7 @@ theorem LinearIndependent.inl_union_inr {s : Set M} {t : Set M'}
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u4}} {M' : Type.{u5}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u4} M] [_inst_3 : AddCommGroup.{u5} M'] [_inst_5 : Module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] [_inst_6 : Module.{u3, u5} R M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)] {v : ι -> M} {v' : ι' -> M'}, (LinearIndependent.{u1, u3, u4} ι R M v (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_5) -> (LinearIndependent.{u2, u3, u5} ι' R M' v' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_6) -> (LinearIndependent.{max u1 u2, u3, max u4 u5} (Sum.{u1, u2} ι ι') R (Prod.{u4, u5} M M') (Sum.elim.{u1, u2, succ (max u4 u5)} ι ι' (Prod.{u4, u5} M M') (Function.comp.{succ u1, succ u4, succ (max u4 u5)} ι M (Prod.{u4, u5} M M') (coeFn.{max (succ u4) (succ (max u4 u5)), max (succ u4) (succ (max u4 u5))} (LinearMap.{u3, u3, u4, max u4 u5} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M (Prod.{u4, u5} M M') (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (Prod.addCommMonoid.{u4, u5} M M' (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)) _inst_5 (Prod.module.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6)) (fun (_x : LinearMap.{u3, u3, u4, max u4 u5} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M (Prod.{u4, u5} M M') (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (Prod.addCommMonoid.{u4, u5} M M' (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)) _inst_5 (Prod.module.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6)) => M -> (Prod.{u4, u5} M M')) (LinearMap.hasCoeToFun.{u3, u3, u4, max u4 u5} R R M (Prod.{u4, u5} M M') (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (Prod.addCommMonoid.{u4, u5} M M' (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)) _inst_5 (Prod.module.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (LinearMap.inl.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6)) v) (Function.comp.{succ 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(Prod.addCommMonoid.{u4, u5} M M' (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)) _inst_6 (Prod.module.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6)) => M' -> (Prod.{u4, u5} M M')) (LinearMap.hasCoeToFun.{u3, u3, u5, max u4 u5} R R M' (Prod.{u4, u5} M M') (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) (Prod.addCommMonoid.{u4, u5} M M' (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)) _inst_6 (Prod.module.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (LinearMap.inr.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6)) v')) (Ring.toSemiring.{u3} R _inst_1) (Prod.addCommMonoid.{u4, u5} M M' (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3)) (Prod.module.{u3, u4, u5} R M M' (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M' _inst_3) _inst_5 _inst_6))
 but is expected to have type
-  forall {ι : Type.{u5}} {ι' : Type.{u2}} {R : Type.{u4}} {M : Type.{u3}} {M' : Type.{u1}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_6 : Module.{u4, u1} R M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)] {v : ι -> M} {v' : ι' -> M'}, (LinearIndependent.{u5, u4, u3} ι R M v (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearIndependent.{u2, u4, u1} ι' R M' v' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_6) -> (LinearIndependent.{max u2 u5, u4, max u3 u1} (Sum.{u5, u2} ι ι') R (Prod.{u3, u1} M M') (Sum.elim.{u5, u2, succ (max u3 u1)} ι ι' (Prod.{u3, u1} M M') (Function.comp.{succ u5, succ u3, succ (max u3 u1)} ι M (Prod.{u3, u1} M M') (FunLike.coe.{max (succ u3) (succ u1), succ u3, max (succ u3) (succ u1)} (LinearMap.{u4, u4, u3, max u1 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))) M (Prod.{u3, u1} M M') (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_5 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => Prod.{u3, u1} M M') _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u3 u1} R R M (Prod.{u3, u1} M M') (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_5 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (LinearMap.inl.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) v) (Function.comp.{succ u2, succ u1, max (succ u3) (succ u1)} ι' M' (Prod.{u3, u1} M M') (FunLike.coe.{max (succ u3) (succ u1), succ u1, max (succ u3) (succ u1)} (LinearMap.{u4, u4, u1, max u1 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))) M' (Prod.{u3, u1} M M') (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_6 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) M' (fun (_x : M') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M') => Prod.{u3, u1} M M') _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, max u3 u1} R R M' (Prod.{u3, u1} M M') (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_6 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (LinearMap.inr.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) v')) (Ring.toSemiring.{u4} R _inst_1) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6))
+  forall {ι : Type.{u5}} {ι' : Type.{u2}} {R : Type.{u4}} {M : Type.{u3}} {M' : Type.{u1}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_6 : Module.{u4, u1} R M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)] {v : ι -> M} {v' : ι' -> M'}, (LinearIndependent.{u5, u4, u3} ι R M v (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearIndependent.{u2, u4, u1} ι' R M' v' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_6) -> (LinearIndependent.{max u2 u5, u4, max u3 u1} (Sum.{u5, u2} ι ι') R (Prod.{u3, u1} M M') (Sum.elim.{u5, u2, succ (max u3 u1)} ι ι' (Prod.{u3, u1} M M') (Function.comp.{succ u5, succ u3, succ (max u3 u1)} ι M (Prod.{u3, u1} M M') (FunLike.coe.{max (succ u3) (succ u1), succ u3, max (succ u3) (succ u1)} (LinearMap.{u4, u4, u3, max u1 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))) M (Prod.{u3, u1} M M') (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_5 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Prod.{u3, u1} M M') _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u3 u1} R R M (Prod.{u3, u1} M M') (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_5 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (LinearMap.inl.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) v) (Function.comp.{succ u2, succ u1, max (succ u3) (succ u1)} ι' M' (Prod.{u3, u1} M M') (FunLike.coe.{max (succ u3) (succ u1), succ u1, max (succ u3) (succ u1)} (LinearMap.{u4, u4, u1, max u1 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))) M' (Prod.{u3, u1} M M') (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_6 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) M' (fun (_x : M') => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M') => Prod.{u3, u1} M M') _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, max u3 u1} R R M' (Prod.{u3, u1} M M') (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) _inst_6 (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (LinearMap.inr.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6)) v')) (Ring.toSemiring.{u4} R _inst_1) (Prod.instAddCommMonoidSum.{u3, u1} M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3)) (Prod.module.{u4, u3, u1} R M M' (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_3) _inst_5 _inst_6))
 Case conversion may be inaccurate. Consider using '#align linear_independent_inl_union_inr' linearIndependent_inl_union_inr'ₓ'. -/
 theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv : LinearIndependent R v)
     (hv' : LinearIndependent R v') :
@@ -1464,7 +1464,7 @@ theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv :
 lean 3 declaration is
   forall (G : Type.{u1}) [_inst_8 : Monoid.{u1} G] (L : Type.{u2}) [_inst_9 : CommRing.{u2} L] [_inst_10 : NoZeroDivisors.{u2} L (Distrib.toHasMul.{u2} L (Ring.toDistrib.{u2} L (CommRing.toRing.{u2} L _inst_9))) (MulZeroClass.toHasZero.{u2} L (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9))))))], LinearIndependent.{max u2 u1, u2, max u1 u2} (MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) => coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) (fun (_x : MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) => G -> L) (MonoidHom.hasCoeToFun.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) f) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9)) (Pi.addCommMonoid.{u1, u2} G (fun (ᾰ : G) => L) (fun (i : G) => AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) (Pi.Function.module.{u1, u2, u2} G L L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9)) (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9))))) (Semiring.toModule.{u2} L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9))))
 but is expected to have type
-  forall (G : Type.{u2}) [_inst_8 : Monoid.{u2} G] (L : Type.{u1}) [_inst_9 : CommRing.{u1} L] [_inst_10 : NoZeroDivisors.{u1} L (NonUnitalNonAssocRing.toMul.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9)))) (CommMonoidWithZero.toZero.{u1} L (CommSemiring.toCommMonoidWithZero.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))], LinearIndependent.{max u2 u1, u1, max u2 u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => L) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G _inst_8)) (MulOneClass.toMul.{u1} L (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (MonoidHom.monoidHomClass.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))))) f) (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (Pi.addCommMonoid.{u2, u1} G (fun (ᾰ : G) => L) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9)))))) (Pi.module.{u2, u1, u1} G (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.14559 : G) => L) L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9))))) (fun (i : G) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))
+  forall (G : Type.{u2}) [_inst_8 : Monoid.{u2} G] (L : Type.{u1}) [_inst_9 : CommRing.{u1} L] [_inst_10 : NoZeroDivisors.{u1} L (NonUnitalNonAssocRing.toMul.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9)))) (CommMonoidWithZero.toZero.{u1} L (CommSemiring.toCommMonoidWithZero.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))], LinearIndependent.{max u2 u1, u1, max u2 u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => L) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G _inst_8)) (MulOneClass.toMul.{u1} L (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (MonoidHom.monoidHomClass.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))))) f) (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (Pi.addCommMonoid.{u2, u1} G (fun (ᾰ : G) => L) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9)))))) (Pi.module.{u2, u1, u1} G (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.14614 : G) => L) L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9))))) (fun (i : G) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))
 Case conversion may be inaccurate. Consider using '#align linear_independent_monoid_hom linearIndependent_monoidHomₓ'. -/
 -- See, for example, Keith Conrad's note
 --  <https://kconrad.math.uconn.edu/blurbs/galoistheory/linearchar.pdf>

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -1523,7 +1523,7 @@ theorem linearIndependent_monoidHom (G : Type _) [Monoid G] (L : Type _) [CommRi
                             a x * (∑ i in insert a s, (g i • i : G → L)) y :=
                         by rw [Finset.sum_apply, Finset.sum_apply, Finset.mul_sum] <;> rfl
                       _ = 0 - a x * 0 := by rw [hg] <;> rfl
-                      _ = 0 := by rw [mul_zero, sub_zero]
+                      _ = 0 := by rw [MulZeroClass.mul_zero, sub_zero]
                       )
                   i his
           -- On the other hand, since `a` is not already in `s`, for any character `i ∈ s`

bump to nightly-2023-03-08-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

10f15343

Diff

@@ -1464,7 +1464,7 @@ theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv :
 lean 3 declaration is
   forall (G : Type.{u1}) [_inst_8 : Monoid.{u1} G] (L : Type.{u2}) [_inst_9 : CommRing.{u2} L] [_inst_10 : NoZeroDivisors.{u2} L (Distrib.toHasMul.{u2} L (Ring.toDistrib.{u2} L (CommRing.toRing.{u2} L _inst_9))) (MulZeroClass.toHasZero.{u2} L (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9))))))], LinearIndependent.{max u2 u1, u2, max u1 u2} (MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) => coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) (fun (_x : MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) => G -> L) (MonoidHom.hasCoeToFun.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) f) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9)) (Pi.addCommMonoid.{u1, u2} G (fun (ᾰ : G) => L) (fun (i : G) => AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) (Pi.Function.module.{u1, u2, u2} G L L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9)) (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9))))) (Semiring.toModule.{u2} L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9))))
 but is expected to have type
-  forall (G : Type.{u2}) [_inst_8 : Monoid.{u2} G] (L : Type.{u1}) [_inst_9 : CommRing.{u1} L] [_inst_10 : NoZeroDivisors.{u1} L (NonUnitalNonAssocRing.toMul.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9)))) (CommMonoidWithZero.toZero.{u1} L (CommSemiring.toCommMonoidWithZero.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))], LinearIndependent.{max u2 u1, u1, max u2 u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => L) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G _inst_8)) (MulOneClass.toMul.{u1} L (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (MonoidHom.monoidHomClass.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))))) f) (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (Pi.addCommMonoid.{u2, u1} G (fun (ᾰ : G) => L) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9)))))) (Pi.module.{u2, u1, u1} G (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.14559 : G) => L) L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9))))) (fun (i : G) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))
+  forall (G : Type.{u2}) [_inst_8 : Monoid.{u2} G] (L : Type.{u1}) [_inst_9 : CommRing.{u1} L] [_inst_10 : NoZeroDivisors.{u1} L (NonUnitalNonAssocRing.toMul.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9)))) (CommMonoidWithZero.toZero.{u1} L (CommSemiring.toCommMonoidWithZero.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))], LinearIndependent.{max u2 u1, u1, max u2 u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => L) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G _inst_8)) (MulOneClass.toMul.{u1} L (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (MonoidHom.monoidHomClass.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))))) f) (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (Pi.addCommMonoid.{u2, u1} G (fun (ᾰ : G) => L) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9)))))) (Pi.module.{u2, u1, u1} G (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.14559 : G) => L) L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9))))) (fun (i : G) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))
 Case conversion may be inaccurate. Consider using '#align linear_independent_monoid_hom linearIndependent_monoidHomₓ'. -/
 -- See, for example, Keith Conrad's note
 --  <https://kconrad.math.uconn.edu/blurbs/galoistheory/linearchar.pdf>

bump to nightly-2023-03-04-12

mathlib commit https://github.com/leanprover-community/mathlib/commit/62e8311c791f02c47451bf14aa2501048e7c2f33

726b2da6

Diff

@@ -114,9 +114,9 @@ variable {R} {v}
 
 /- warning: linear_independent_iff -> linearIndependent_iff is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2], Iff (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), (Eq.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u3, u2} ι M R _inst_1 _inst_2 _inst_5 v) l) (OfNat.ofNat.{u3} M 0 (OfNat.mk.{u3} M 0 (Zero.zero.{u3} M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2))))))) -> (Eq.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) l (OfNat.ofNat.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) 0 (OfNat.mk.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) 0 (Zero.zero.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Finsupp.hasZero.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))))
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2], Iff (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))), (Eq.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u3, u2} ι M R _inst_1 _inst_2 _inst_5 v) l) (OfNat.ofNat.{u3} M 0 (OfNat.mk.{u3} M 0 (Zero.zero.{u3} M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2))))))) -> (Eq.{max (succ u1) (succ u2)} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) l (OfNat.ofNat.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) 0 (OfNat.mk.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) 0 (Zero.zero.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Finsupp.zero.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι 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_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.zero.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) l (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.zero.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_iff linearIndependent_iffₓ'. -/
 theorem linearIndependent_iff : LinearIndependent R v ↔ ∀ l, Finsupp.total ι M R v l = 0 → l = 0 :=
   by simp [LinearIndependent, LinearMap.ker_eq_bot']
@@ -506,9 +506,9 @@ section Subtype
 
 /- warning: linear_independent_comp_subtype -> linearIndependent_comp_subtype is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, Iff (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))), (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) 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 Case conversion may be inaccurate. Consider using '#align linear_independent_comp_subtype linearIndependent_comp_subtypeₓ'. -/
 theorem linearIndependent_comp_subtype {s : Set ι} :
     LinearIndependent R (v ∘ coe : s → M) ↔
@@ -531,9 +531,9 @@ theorem linearIndependent_comp_subtype {s : Set ι} :
 
 /- warning: linear_dependent_comp_subtype' -> linearDependent_comp_subtype' is a dubious translation:
 lean 3 declaration is
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) 0 (OfNat.mk.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) 0 (Zero.zero.{max u1 u2} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Finsupp.zero.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))))))))
 but is expected to have type
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) f (Finsupp.supported.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s)) (And (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 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M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v) f) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) _inst_2))))) (Ne.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) f (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.zero.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, Iff (Not (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5)) (Exists.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (f : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => And (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R 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_inst_1))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => M) f) _inst_2))))) (Ne.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) f (OfNat.ofNat.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) 0 (Zero.toOfNat0.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.zero.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))))))
 Case conversion may be inaccurate. Consider using '#align linear_dependent_comp_subtype' linearDependent_comp_subtype'ₓ'. -/
 theorem linearDependent_comp_subtype' {s : Set ι} :
     ¬LinearIndependent R (v ∘ coe : s → M) ↔
@@ -543,9 +543,9 @@ theorem linearDependent_comp_subtype' {s : Set ι} :
 
 /- warning: linear_dependent_comp_subtype -> linearDependent_comp_subtype is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, Iff (Not (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5)) (Exists.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (fun (f : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) => And (Membership.mem.{max u3 u2, max u2 u3} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R 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 Case conversion may be inaccurate. Consider using '#align linear_dependent_comp_subtype linearDependent_comp_subtypeₓ'. -/
 /-- A version of `linear_dependent_comp_subtype'` with `finsupp.total` unfolded. -/
 theorem linearDependent_comp_subtype {s : Set ι} :
@@ -556,9 +556,9 @@ theorem linearDependent_comp_subtype {s : Set ι} :
 
 /- warning: linear_independent_subtype -> linearIndependent_subtype is a dubious translation:
 lean 3 declaration is
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_5) (fun (_x : LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) => (Finsupp.{u2, u1} M R 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 but is expected to have type
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+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M s) R M (fun (x : Set.Elem.{u2} M s) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) x) _inst_1 _inst_2 _inst_5) (forall (l : Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))), (Membership.mem.{max u1 u2, max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) l (Finsupp.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (fun (_x : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_2 _inst_5 (id.{succ u2} M)) l) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) => M) l) _inst_2))))) -> (Eq.{max (succ u1) (succ u2)} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) l (OfNat.ofNat.{max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) 0 (Zero.toOfNat0.{max u1 u2} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Finsupp.zero.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_subtype linearIndependent_subtypeₓ'. -/
 theorem linearIndependent_subtype {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
@@ -570,7 +570,7 @@ theorem linearIndependent_subtype {s : Set M} :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] {s : Set.{u1} ι}, Iff (LinearIndependent.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) R M (Function.comp.{succ u1, succ u1, succ u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι M v ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeSubtype.{succ u1} ι (fun (x : ι) => Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) x s))))))) _inst_1 _inst_2 _inst_5) (Disjoint.{max u1 u2} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) (Submodule.setLike.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))) (Submodule.orderBot.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.supported.{u1, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s) (LinearMap.ker.{u2, u2, max u1 u2, u3, max (max u1 u2) u3} R R (Finsupp.{u1, u2} ι R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5) (LinearMap.semilinearMapClass.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u1, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u1, u3, u2} ι M R _inst_1 _inst_2 _inst_5 v)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, Iff (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5) (Disjoint.{max u2 u3} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Submodule.completeLattice.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.supported.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s) (LinearMap.ker.{u2, u2, max u3 u2, u1, max (max u3 u2) u1} R R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι 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_5) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v)))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, Iff (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5) (Disjoint.{max u2 u3} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u2, max u2 u3} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Submodule.completeLattice.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (Finsupp.supported.{u3, u2, u2} ι R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1) s) (LinearMap.ker.{u2, u2, max u3 u2, u1, max (max u3 u2) u1} R R (Finsupp.{u3, u2} ι R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.module.{u3, u2, u2} ι 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_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Finsupp.total.{u3, u1, u2} ι M R _inst_1 _inst_2 _inst_5 v)))
 Case conversion may be inaccurate. Consider using '#align linear_independent_comp_subtype_disjoint linearIndependent_comp_subtype_disjointₓ'. -/
 theorem linearIndependent_comp_subtype_disjoint {s : Set ι} :
     LinearIndependent R (v ∘ coe : s → M) ↔
@@ -582,7 +582,7 @@ theorem linearIndependent_comp_subtype_disjoint {s : Set ι} :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x s))))) x) _inst_1 _inst_2 _inst_5) (Disjoint.{max u2 u1} (Submodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (SetLike.partialOrder.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) (Submodule.setLike.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) (Submodule.orderBot.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s) (LinearMap.ker.{u1, u1, max u2 u1, u2, max u2 u1} R R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, u2} R R (Finsupp.{u2, u1} M R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_2 _inst_5 (id.{succ u2} M))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M s) R M (fun (x : Set.Elem.{u2} M s) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) x) _inst_1 _inst_2 _inst_5) (Disjoint.{max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Submodule.completeLattice.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s) (LinearMap.ker.{u1, u1, max u1 u2, u2, max u1 u2} R R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u1, u1} M 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_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_2 _inst_5 (id.{succ u2} M))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M s) R M (fun (x : Set.Elem.{u2} M s) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) x) _inst_1 _inst_2 _inst_5) (Disjoint.{max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{max u1 u2} (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Submodule.completeLattice.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s) (LinearMap.ker.{u1, u1, max u1 u2, u2, max u1 u2} R R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u1 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u1 u2, u2} R R (Finsupp.{u2, u1} M R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) M _inst_1 _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.module.{u2, u1, u1} M 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_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finsupp.total.{u2, u2, u1} M M R _inst_1 _inst_2 _inst_5 (id.{succ u2} M))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_subtype_disjoint linearIndependent_subtype_disjointₓ'. -/
 theorem linearIndependent_subtype_disjoint {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
@@ -594,7 +594,7 @@ theorem linearIndependent_subtype_disjoint {s : Set M} :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x s))))) x) _inst_1 _inst_2 _inst_5) (Eq.{succ (max u2 u1)} (Submodule.{u1, max u2 u1} R (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) (Submodule.setLike.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) _inst_1 (Submodule.addCommMonoid.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.module.{u1, max u2 u1} R (Finsupp.{u2, u1} M R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) _inst_1 (Submodule.addCommMonoid.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.module.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M s) R M (fun (x : Set.Elem.{u2} M s) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) x) _inst_1 _inst_2 _inst_5) (Eq.{max (succ u1) (succ u2)} (Submodule.{u1, max u1 u2} R (Subtype.{succ (max u2 u1)} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (x : Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => Membership.mem.{max u2 u1, max u2 u1} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.{u1, max u1 u2} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) 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(Semiring.toModule.{u1} R _inst_1) s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Iff (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} M s) R M (fun (x : Set.Elem.{u2} M s) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) x) _inst_1 _inst_2 _inst_5) (Eq.{max (succ u1) (succ u2)} (Submodule.{u1, max u1 u2} R (Subtype.{succ (max u2 u1)} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (x : Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => Membership.mem.{max u2 u1, 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.instSetLikeSubmodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R 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_inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R 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(Semiring.toModule.{u1} R _inst_1)) (Finsupp.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))) (Submodule.instBotSubmodule.{u1, max u1 u2} R (Subtype.{succ (max u2 u1)} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (fun (x : Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) => Membership.mem.{max u2 u1, max u2 u1} (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Submodule.instSetLikeSubmodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) x (Finsupp.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, max u2 u1} R (Finsupp.{u2, u1} M R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) _inst_1 (Finsupp.addCommMonoid.{u2, u1} M R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.module.{u2, u1, u1} M 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.supported.{u2, u1, u1} M R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1) s)))))
 Case conversion may be inaccurate. Consider using '#align linear_independent_iff_total_on linearIndependent_iff_totalOnₓ'. -/
 theorem linearIndependent_iff_totalOn {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔ (Finsupp.totalOn M M R id s).ker = ⊥ := by
@@ -700,7 +700,7 @@ variable {a b : R} {x y : M}
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], Iff (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Function.Injective.{max (succ u1) (succ u2), succ u3} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u1, u3, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 v)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], Iff (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Function.Injective.{max (succ u3) (succ u2), succ u1} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v)))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], Iff (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Function.Injective.{max (succ u3) (succ u2), succ u1} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v)))
 Case conversion may be inaccurate. Consider using '#align linear_independent_iff_injective_total linearIndependent_iff_injective_totalₓ'. -/
 theorem linearIndependent_iff_injective_total :
     LinearIndependent R v ↔ Function.Injective (Finsupp.total ι M R v) :=
@@ -712,7 +712,7 @@ theorem linearIndependent_iff_injective_total :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (Function.Injective.{max (succ u1) (succ u2), succ u3} (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u1, u3, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 v)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (Function.Injective.{max (succ u3) (succ u2), succ u1} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v)))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (Function.Injective.{max (succ u3) (succ u2), succ u1} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v)))
 Case conversion may be inaccurate. Consider using '#align linear_independent.injective_total LinearIndependent.injective_totalₓ'. -/
 alias linearIndependent_iff_injective_total ↔ LinearIndependent.injective_total _
 #align linear_independent.injective_total LinearIndependent.injective_total
@@ -945,7 +945,7 @@ theorem LinearIndependent.not_mem_span_image [Nontrivial R] (hv : LinearIndepend
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_8 : Nontrivial.{u2} R], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall {x : ι} (f : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))), (Not (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) x (Finsupp.support.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) f))) -> (Ne.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) => (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u1, u3, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 v) f) (v x)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Nontrivial.{u2} R], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall {x : ι} (f : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))), (Not (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) x (Finsupp.support.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) f))) -> (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) f) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v) f) (v x)))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Nontrivial.{u2} R], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall {x : ι} (f : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))), (Not (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) x (Finsupp.support.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) f))) -> (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) f) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v) f) (v x)))
 Case conversion may be inaccurate. Consider using '#align linear_independent.total_ne_of_not_mem_support LinearIndependent.total_ne_of_not_mem_supportₓ'. -/
 theorem LinearIndependent.total_ne_of_not_mem_support [Nontrivial R] (hv : LinearIndependent R v)
     {x : ι} (f : ι →₀ R) (h : x ∉ f.support) : Finsupp.total ι M R v f ≠ v x :=
@@ -1096,7 +1096,7 @@ variable (hv : LinearIndependent R v)
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearEquiv.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearIndependent.totalEquiv._proof_1.{u2} R _inst_1) (LinearIndependent.totalEquiv._proof_2.{u2} R _inst_1) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))))
 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearEquiv.{u2, u2, max u2 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) x (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))))
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearEquiv.{u2, u2, max u2 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) x (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.total_equiv LinearIndependent.totalEquivₓ'. -/
 /-- Canonical isomorphism between linear combinations and the span of linearly independent vectors.
 -/
@@ -1121,7 +1121,7 @@ def LinearIndependent.totalEquiv (hv : LinearIndependent R v) : (ι →₀ R) 
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))))
 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearMap.{u2, u2, u3, max u2 u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) x (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)))
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearMap.{u2, u2, u3, max u2 u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) x (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr LinearIndependent.reprₓ'. -/
 /-- Linear combination representing a vector in the span of linearly independent vectors.
 
@@ -1136,7 +1136,7 @@ def LinearIndependent.repr (hv : LinearIndependent R v) : span R (range v) →
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))), Eq.{succ u3} M (coeFn.{max (succ (max u1 u2)) (succ 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(Ring.toSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) 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(Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv) x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) M (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) M (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) M (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} 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 but is expected to have type
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+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))), Eq.{succ u2} 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_inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv) x)) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) x)
 Case conversion may be inaccurate. Consider using '#align linear_independent.total_repr LinearIndependent.total_reprₓ'. -/
 @[simp]
 theorem LinearIndependent.total_repr (x) : Finsupp.total ι M R v (hv.repr x) = x :=
@@ -1147,7 +1147,7 @@ theorem LinearIndependent.total_repr (x) : Finsupp.total ι M R v (hv.repr x) =
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5), Eq.{succ u3} (LinearMap.{u2, u2, u3, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) M (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) _inst_5) (LinearMap.comp.{u2, u2, u2, u3, max u1 u2, u3} R R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.right_ids.{u2, u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u1, u3, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 v) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Submodule.subtype.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} 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))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) M (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) _inst_5) (LinearMap.comp.{u1, u1, u1, u2, max u3 u1, u2} R R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} 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)))) (Finsupp.total.{u3, u2, u1} ι M R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 v) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Submodule.subtype.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} 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))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) M (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) _inst_5) (LinearMap.comp.{u1, u1, u1, u2, max u3 u1, u2} R R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} 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)))) (Finsupp.total.{u3, u2, u1} ι M R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 v) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Submodule.subtype.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))
 Case conversion may be inaccurate. Consider using '#align linear_independent.total_comp_repr LinearIndependent.total_comp_reprₓ'. -/
 theorem LinearIndependent.total_comp_repr :
     (Finsupp.total ι M R v).comp hv.repr = Submodule.subtype _ :=
@@ -1158,7 +1158,7 @@ theorem LinearIndependent.total_comp_repr :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5), Eq.{succ u3} (Submodule.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (LinearMap.ker.{u2, u2, u3, max u1 u2, max u3 u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.semilinearMapClass.{u2, u2, u3, max u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Bot.bot.{u3} (Submodule.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Submodule.hasBot.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5), Eq.{succ u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (LinearMap.ker.{u1, u1, u2, max u3 u1, max (max u3 u1) u2} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, max u1 u3} 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))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Bot.bot.{u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Submodule.instBotSubmodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))))
+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5), Eq.{succ u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (LinearMap.ker.{u1, u1, u2, max u3 u1, max (max u3 u1) u2} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, max u1 u3} 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))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Bot.bot.{u2} (Submodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} 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_inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Submodule.instBotSubmodule.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))))
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_ker LinearIndependent.repr_kerₓ'. -/
 theorem LinearIndependent.repr_ker : hv.repr.ker = ⊥ := by
   rw [LinearIndependent.repr, LinearEquiv.ker]
@@ -1168,7 +1168,7 @@ theorem LinearIndependent.repr_ker : hv.repr.ker = ⊥ := by
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5), Eq.{succ (max u1 u2)} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.range.{u2, u2, u3, max u1 u2, max u3 u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R 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(Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearMap.semilinearMapClass.{u2, u2, u3, max u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M 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(Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Top.top.{max u1 u2} (Submodule.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.hasTop.{u2, max u1 u2} R (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5), Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1))) (LinearMap.range.{u2, u2, u1, max u3 u2, max (max u3 u2) u1} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, max u2 u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1))) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Top.top.{max u3 u2} (Submodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1))) (Submodule.instTopSubmodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1))))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5), Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1))) (LinearMap.range.{u2, u2, u1, max u3 u2, max (max u3 u2) u1} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, max u2 u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R 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 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_range LinearIndependent.repr_rangeₓ'. -/
 theorem LinearIndependent.repr_range : hv.repr.range = ⊤ := by
   rw [LinearIndependent.repr, LinearEquiv.range]
@@ -1178,7 +1178,7 @@ theorem LinearIndependent.repr_range : hv.repr.range = ⊤ := by
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) {l : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))} {x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) 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 but is expected to have type
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(instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv) x) l)
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) {l : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))} {x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => M) l) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) 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_inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Finsupp.total.{u3, u1, u2} ι M R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 v) l) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) x)) -> (Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) 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_inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv) x) l)
 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq LinearIndependent.repr_eqₓ'. -/
 theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M R v l = ↑x) :
     hv.repr x = l :=
@@ -1200,7 +1200,7 @@ theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M
 lean 3 declaration is
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 but is expected to have type
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+  forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} {v : ι -> M} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (hv : LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (i : ι) (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))), 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 Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq_single LinearIndependent.repr_eq_singleₓ'. -/
 theorem LinearIndependent.repr_eq_single (i) (x) (hx : ↑x = v i) : hv.repr x = Finsupp.single i 1 :=
   by
@@ -1212,7 +1212,7 @@ theorem LinearIndependent.repr_eq_single (i) (x) (hx : ↑x = v i) : hv.repr x =
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) [_inst_8 : Nontrivial.{u2} R] (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))), Eq.{max (succ u3) (succ u2)} (Finsupp.{u3, u2} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) (Set.range.{u3, succ u1} M ι v)) R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) (Span.repr.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v) x) (Finsupp.equivMapDomain.{u1, u3, u2} ι (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) (Set.range.{u3, succ u1} M ι v)) R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Equiv.ofInjective.{succ u1, u3} ι M v (LinearIndependent.injective.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 _inst_8 hv)) (coeFn.{max (succ u3) (succ (max u1 u2)), max (succ u3) (succ (max u1 u2))} (LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) => (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) -> (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))))) (LinearMap.hasCoeToFun.{u2, u2, u3, max u1 u2} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 hv) x))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) [_inst_8 : Nontrivial.{u2} R] (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))), Eq.{max (succ u2) (succ u1)} (Finsupp.{u1, u2} (Set.Elem.{u1} M (Set.range.{u1, succ u3} M ι v)) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Span.repr.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v) x) (Finsupp.equivMapDomain.{u3, u1, u2} ι (Set.Elem.{u1} M (Set.range.{u1, succ u3} M ι v)) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Equiv.ofInjective.{succ u3, u1} ι M v (LinearIndependent.injective.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 _inst_8 hv)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u1, max (succ u3) (succ u2)} (LinearMap.{u2, u2, u1, max u2 u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u1} M (fun (x : M) => 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(instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv) x))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (hv : LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) [_inst_8 : Nontrivial.{u2} R] (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))), Eq.{max (succ u2) (succ u1)} (Finsupp.{u1, u2} (Set.Elem.{u1} M (Set.range.{u1, succ u3} M ι v)) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Span.repr.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v) x) (Finsupp.equivMapDomain.{u3, u1, u2} ι (Set.Elem.{u1} M (Set.range.{u1, succ u3} M ι v)) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Equiv.ofInjective.{succ u3, u1} ι M v (LinearIndependent.injective.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5 _inst_8 hv)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u1, max (succ u3) (succ u2)} (LinearMap.{u2, u2, u1, max u2 u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) => Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u3 u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M ι v))) (Finsupp.module.{u3, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (LinearIndependent.repr.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5 hv) x))
 Case conversion may be inaccurate. Consider using '#align linear_independent.span_repr_eq LinearIndependent.span_repr_eqₓ'. -/
 theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
     Span.repr R (Set.range v) x = (hv.repr x).equivMapDomain (Equiv.ofInjective _ hv.Injective) :=

bump to nightly-2023-03-03-10

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

04b5c979

Diff

@@ -791,7 +791,7 @@ theorem LinearIndependent.image {ι} {s : Set ι} {f : ι → M}
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {G : Type.{u4}} [hG : Group.{u4} G] [_inst_8 : DistribMulAction.{u4, u2} G R (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (NonAssocRing.toAddGroupWithOne.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))] [_inst_9 : DistribMulAction.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))] [_inst_10 : IsScalarTower.{u4, u2, u3} G R M (SMulZeroClass.toHasSmul.{u4, u2} G R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (NonAssocRing.toAddGroupWithOne.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (DistribSMul.toSmulZeroClass.{u4, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (NonAssocRing.toAddGroupWithOne.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{u4, u2} G R (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (NonAssocRing.toAddGroupWithOne.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) _inst_8))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)))) (SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u4, u2, u3} G R M (SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u1, u2, u3} ι R M (SMul.smul.{max u1 u4, max u1 u3} (ι -> G) (ι -> M) (Pi.smul'.{u1, u4, u3} ι (fun (ᾰ : ι) => G) (fun (ᾰ : ι) => M) (fun (i : ι) => SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9)))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)
 but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {G : Type.{u3}} [hG : Group.{u3} G] [_inst_8 : DistribMulAction.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))] [_inst_9 : DistribMulAction.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))] [_inst_10 : IsScalarTower.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u2} G R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (DistribSMul.toSMulZeroClass.{u3, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))) (DistribMulAction.toDistribSMul.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1))) _inst_8))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u4, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u4, u2, u1} ι R M (HSMul.hSMul.{max u4 u3, max u4 u1, max u4 u1} (ι -> G) (ι -> M) (ι -> M) (instHSMul.{max u4 u3, max u4 u1} (ι -> G) (ι -> M) (Pi.smul'.{u4, u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6559 : ι) => G) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6553 : ι) => M) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
+  forall {ι : Type.{u4}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {G : Type.{u3}} [hG : Group.{u3} G] [_inst_8 : DistribMulAction.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))] [_inst_9 : DistribMulAction.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))] [_inst_10 : IsScalarTower.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u2} G R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (DistribSMul.toSMulZeroClass.{u3, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))) (DistribMulAction.toDistribSMul.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1))) _inst_8))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u4, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u4, u2, u1} ι R M (HSMul.hSMul.{max u4 u3, max u4 u1, max u4 u1} (ι -> G) (ι -> M) (ι -> M) (instHSMul.{max u4 u3, max u4 u1} (ι -> G) (ι -> M) (Pi.smul'.{u4, u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6561 : ι) => G) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6555 : ι) => M) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent.group_smul LinearIndependent.group_smulₓ'. -/
 theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulAction G R]
     [DistribMulAction G M] [IsScalarTower G R M] [SMulCommClass G R M] {v : ι → M}
@@ -812,7 +812,7 @@ theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulActi
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {v : ι -> M}, (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall (w : ι -> (Units.{u2} R (Ring.toMonoid.{u2} R _inst_1))), LinearIndependent.{u1, u2, u3} ι R M (SMul.smul.{max u1 u2, max u1 u3} (ι -> (Units.{u2} R (Ring.toMonoid.{u2} R _inst_1))) (ι -> M) (Pi.smul'.{u1, u2, u3} ι (fun (ᾰ : ι) => Units.{u2} R (Ring.toMonoid.{u2} R _inst_1)) (fun (ᾰ : ι) => M) (fun (i : ι) => Units.hasSmul.{u2, u3} R M (Ring.toMonoid.{u2} R _inst_1) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {v : ι -> M}, (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))), LinearIndependent.{u3, u2, u1} ι R M (HSMul.hSMul.{max u3 u2, max u3 u1, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (ι -> M) (instHSMul.{max u3 u2, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6789 : ι) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6783 : ι) => M) (fun (i : ι) => Units.instSMulUnits.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {v : ι -> M}, (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))), LinearIndependent.{u3, u2, u1} ι R M (HSMul.hSMul.{max u3 u2, max u3 u1, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (ι -> M) (instHSMul.{max u3 u2, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6791 : ι) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6785 : ι) => M) (fun (i : ι) => Units.instSMulUnits.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_independent.units_smul LinearIndependent.units_smulₓ'. -/
 -- This lemma cannot be proved with `linear_independent.group_smul` since the action of
 -- `Rˣ` on `R` is not commutative.
@@ -1464,7 +1464,7 @@ theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv :
 lean 3 declaration is
   forall (G : Type.{u1}) [_inst_8 : Monoid.{u1} G] (L : Type.{u2}) [_inst_9 : CommRing.{u2} L] [_inst_10 : NoZeroDivisors.{u2} L (Distrib.toHasMul.{u2} L (Ring.toDistrib.{u2} L (CommRing.toRing.{u2} L _inst_9))) (MulZeroClass.toHasZero.{u2} L (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9))))))], LinearIndependent.{max u2 u1, u2, max u1 u2} (MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) => coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) (fun (_x : MonoidHom.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) => G -> L) (MonoidHom.hasCoeToFun.{u1, u2} G L (Monoid.toMulOneClass.{u1} G _inst_8) (MulZeroOneClass.toMulOneClass.{u2} L (NonAssocSemiring.toMulZeroOneClass.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) f) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9)) (Pi.addCommMonoid.{u1, u2} G (fun (ᾰ : G) => L) (fun (i : G) => AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9)))))) (Pi.Function.module.{u1, u2, u2} G L L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9)) (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (CommRing.toRing.{u2} L _inst_9))))) (Semiring.toModule.{u2} L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_9))))
 but is expected to have type
-  forall (G : Type.{u2}) [_inst_8 : Monoid.{u2} G] (L : Type.{u1}) [_inst_9 : CommRing.{u1} L] [_inst_10 : NoZeroDivisors.{u1} L (NonUnitalNonAssocRing.toMul.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9)))) (CommMonoidWithZero.toZero.{u1} L (CommSemiring.toCommMonoidWithZero.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))], LinearIndependent.{max u2 u1, u1, max u2 u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => L) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G _inst_8)) (MulOneClass.toMul.{u1} L (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (MonoidHom.monoidHomClass.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))))) f) (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (Pi.addCommMonoid.{u2, u1} G (fun (ᾰ : G) => L) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9)))))) (Pi.module.{u2, u1, u1} G (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.14557 : G) => L) L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9))))) (fun (i : G) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))
+  forall (G : Type.{u2}) [_inst_8 : Monoid.{u2} G] (L : Type.{u1}) [_inst_9 : CommRing.{u1} L] [_inst_10 : NoZeroDivisors.{u1} L (NonUnitalNonAssocRing.toMul.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9)))) (CommMonoidWithZero.toZero.{u1} L (CommSemiring.toCommMonoidWithZero.{u1} L (CommRing.toCommSemiring.{u1} L _inst_9)))], LinearIndependent.{max u2 u1, u1, max u2 u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) L (G -> L) (fun (f : MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => L) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G _inst_8)) (MulOneClass.toMul.{u1} L (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))) G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9))))) (MonoidHom.monoidHomClass.{u2, u1} G L (Monoid.toMulOneClass.{u2} G _inst_8) (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)))))))) f) (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (Pi.addCommMonoid.{u2, u1} G (fun (ᾰ : G) => L) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9)))))) (Pi.module.{u2, u1, u1} G (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.14559 : G) => L) L (Ring.toSemiring.{u1} L (CommRing.toRing.{u1} L _inst_9)) (fun (i : G) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonUnitalRing.toNonUnitalNonAssocRing.{u1} L (NonUnitalCommRing.toNonUnitalRing.{u1} L (CommRing.toNonUnitalCommRing.{u1} L _inst_9))))) (fun (i : G) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} L (CommRing.toRing.{u1} L _inst_9)))
 Case conversion may be inaccurate. Consider using '#align linear_independent_monoid_hom linearIndependent_monoidHomₓ'. -/
 -- See, for example, Keith Conrad's note
 --  <https://kconrad.math.uconn.edu/blurbs/galoistheory/linearchar.pdf>

bump to nightly-2023-03-01-20

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

20cadee0

Diff

@@ -140,10 +140,10 @@ theorem linearIndependent_iff' :
         g i = (Finsupp.lapply i : (ι →₀ R) →ₗ[R] R) (Finsupp.single i (g i)) := by
           rw [Finsupp.lapply_apply, Finsupp.single_eq_same]
         _ = ∑ j in s, (Finsupp.lapply i : (ι →₀ R) →ₗ[R] R) (Finsupp.single j (g j)) :=
-          Eq.symm <|
+          (Eq.symm <|
             Finset.sum_eq_single i
               (fun j hjs hji => by rw [Finsupp.lapply_apply, Finsupp.single_eq_of_ne hji])
-              fun hnis => hnis.elim his
+              fun hnis => hnis.elim his)
         _ = (∑ j in s, Finsupp.single j (g j)) i :=
           (Finsupp.lapply i : (ι →₀ R) →ₗ[R] R).map_sum.symm
         _ = 0 := Finsupp.ext_iff.1 h i
@@ -159,7 +159,7 @@ lean 3 declaration is
 but is expected to have type
   forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) (forall (s : Finset.{u3} ι) (g : ι -> R), (forall (i : ι), (Not (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s)) -> (Eq.{succ u2} R (g i) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))) -> (Eq.{succ u1} M (Finset.sum.{u1, u3} M ι _inst_2 s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (g i) (v i))) (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))) -> (forall (i : ι), Eq.{succ u2} R (g i) (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_independent_iff'' linearIndependent_iff''ₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (i «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
 theorem linearIndependent_iff'' :
     LinearIndependent R v ↔
       ∀ (s : Finset ι) (g : ι → R) (hg : ∀ (i) (_ : i ∉ s), g i = 0),
@@ -633,7 +633,7 @@ theorem LinearIndependent.mono {t s : Set M} (h : t ⊆ s) :
 #align linear_independent.mono LinearIndependent.mono
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print linearIndependent_of_finite /-
 theorem linearIndependent_of_finite (s : Set M)
     (H : ∀ (t) (_ : t ⊆ s), Set.Finite t → LinearIndependent R (fun x => x : t → M)) :
@@ -1321,7 +1321,7 @@ lean 3 declaration is
 but is expected to have type
   forall {ι : Type.{u3}} (R : Type.{u2}) {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (s : ι -> M), Exists.{succ u3} (Set.{u3} ι) (fun (I : Set.{u3} ι) => And (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι I) R M (fun (x : Set.Elem.{u3} ι I) => s (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x I) x)) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (forall (i : ι), (Not (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I)) -> (Exists.{succ u2} R (fun (a : R) => And (Ne.{succ u2} R a (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) (HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))) a (s i)) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.image.{u3, u1} ι M s I)))))))
 Case conversion may be inaccurate. Consider using '#align exists_maximal_independent exists_maximal_independentₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (i «expr ∉ » I) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » I) -/
 theorem exists_maximal_independent (s : ι → M) :
     ∃ I : Set ι,
       (LinearIndependent R fun x : I => s x) ∧
@@ -1500,7 +1500,7 @@ theorem linearIndependent_monoidHom (G : Type _) [Monoid G] (L : Type _) [CommRi
                           ∑ i in s, (g i * i x - g i * a x) * i y :=
                         Finset.sum_apply _ _ _
                       _ = ∑ i in s, g i * i x * i y - g i * a x * i y :=
-                        Finset.sum_congr rfl fun _ _ => sub_mul _ _ _
+                        (Finset.sum_congr rfl fun _ _ => sub_mul _ _ _)
                       _ = (∑ i in s, g i * i x * i y) - ∑ i in s, g i * a x * i y :=
                         Finset.sum_sub_distrib
                       _ =
@@ -1514,10 +1514,10 @@ theorem linearIndependent_monoidHom (G : Type _) [Monoid G] (L : Type _) [CommRi
                       _ =
                           (∑ i in insert a s, g i * i (x * y)) -
                             ∑ i in insert a s, a x * (g i * i y) :=
-                        congr
+                        (congr
                           (congr_arg Sub.sub
                             (Finset.sum_congr rfl fun i _ => by rw [i.map_mul, mul_assoc]))
-                          (Finset.sum_congr rfl fun _ _ => by rw [mul_assoc, mul_left_comm])
+                          (Finset.sum_congr rfl fun _ _ => by rw [mul_assoc, mul_left_comm]))
                       _ =
                           (∑ i in insert a s, (g i • i : G → L)) (x * y) -
                             a x * (∑ i in insert a s, (g i • i : G → L)) y :=
@@ -1873,7 +1873,7 @@ lean 3 declaration is
 but is expected to have type
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {s : Set.{u2} V} {t : Set.{u2} V}, (LinearIndependent.{u2, u1, u2} (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s)) K V (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) -> (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) s t) -> (Exists.{succ u2} (Set.{u2} V) (fun (b : Set.{u2} V) => Exists.{0} (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) b t) (fun (H : HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) b t) => And (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) s b) (And (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) t (SetLike.coe.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 b))) (LinearIndependent.{u2, u1, u2} (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x b)) K V (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x b)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)))))
 Case conversion may be inaccurate. Consider using '#align exists_linear_independent_extension exists_linearIndependent_extensionₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (b «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ⊆ » t) -/
 theorem exists_linearIndependent_extension (hs : LinearIndependent K (coe : s → V)) (hst : s ⊆ t) :
     ∃ (b : _)(_ : b ⊆ t), s ⊆ b ∧ t ⊆ span K b ∧ LinearIndependent K (coe : b → V) :=
   by
@@ -1898,7 +1898,7 @@ lean 3 declaration is
 but is expected to have type
   forall (K : Type.{u1}) {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (t : Set.{u2} V), Exists.{succ u2} (Set.{u2} V) (fun (b : Set.{u2} V) => Exists.{0} (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) b t) (fun (H : HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) b t) => And (Eq.{succ u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 b) (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 t)) (LinearIndependent.{u2, u1, u2} (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x b)) K V (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x b)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4)))
 Case conversion may be inaccurate. Consider using '#align exists_linear_independent exists_linearIndependentₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (b «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ⊆ » t) -/
 theorem exists_linearIndependent :
     ∃ (b : _)(_ : b ⊆ t), span K b = span K t ∧ LinearIndependent K (coe : b → V) :=
   by

bump to nightly-2023-02-25-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/271bf175e6c51b8d31d6c0107b7bb4a967c7277e

39ef98db

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp, Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.linear_independent
-! leanprover-community/mathlib commit 6d584f1709bedbed9175bd9350df46599bdd7213
+! leanprover-community/mathlib commit ef7acf407d265ad4081c8998687e994fa80ba70c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.SetTheory.Cardinal.Basic
 
 # Linear independence
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines linear independence in a module or vector space.
 
 It is inspired by Isabelle/HOL's linear algebra, and hence indirectly by HOL Light.

bump to nightly-2023-02-23-14

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

5ac40b03

Diff

@@ -100,17 +100,31 @@ variable {a b : R} {x y : M}
 
 variable (R) (v)
 
+#print LinearIndependent /-
 /-- `linear_independent R v` states the family of vectors `v` is linearly independent over `R`. -/
 def LinearIndependent : Prop :=
   (Finsupp.total ι M R v).ker = ⊥
 #align linear_independent LinearIndependent
+-/
 
 variable {R} {v}
 
+/- warning: linear_independent_iff -> linearIndependent_iff is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align linear_independent_iff linearIndependent_iffₓ'. -/
 theorem linearIndependent_iff : LinearIndependent R v ↔ ∀ l, Finsupp.total ι M R v l = 0 → l = 0 :=
   by simp [LinearIndependent, LinearMap.ker_eq_bot']
 #align linear_independent_iff linearIndependent_iff
 
+/- warning: linear_independent_iff' -> linearIndependent_iff' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align linear_independent_iff' linearIndependent_iff'ₓ'. -/
 theorem linearIndependent_iff' :
     LinearIndependent R v ↔
       ∀ s : Finset ι, ∀ g : ι → R, (∑ i in s, g i • v i) = 0 → ∀ i ∈ s, g i = 0 :=
@@ -136,6 +150,12 @@ theorem linearIndependent_iff' :
         by_contradiction fun hni => hni <| hf _ _ hl _ <| Finsupp.mem_support_iff.2 hni⟩
 #align linear_independent_iff' linearIndependent_iff'
 
+/- warning: linear_independent_iff'' -> linearIndependent_iff'' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align linear_independent_iff'' linearIndependent_iff''ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (i «expr ∉ » s) -/
 theorem linearIndependent_iff'' :
     LinearIndependent R v ↔
@@ -150,6 +170,12 @@ theorem linearIndependent_iff'' :
       exact (if_pos hi).symm⟩
 #align linear_independent_iff'' linearIndependent_iff''
 
+/- warning: not_linear_independent_iff -> not_linearIndependent_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align not_linear_independent_iff not_linearIndependent_iffₓ'. -/
 theorem not_linearIndependent_iff :
     ¬LinearIndependent R v ↔
       ∃ s : Finset ι, ∃ g : ι → R, (∑ i in s, g i • v i) = 0 ∧ ∃ i ∈ s, g i ≠ 0 :=
@@ -158,6 +184,12 @@ theorem not_linearIndependent_iff :
   simp only [exists_prop, not_forall]
 #align not_linear_independent_iff not_linearIndependent_iff
 
+/- warning: fintype.linear_independent_iff -> Fintype.linearIndependent_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fintype.linear_independent_iff Fintype.linearIndependent_iffₓ'. -/
 theorem Fintype.linearIndependent_iff [Fintype ι] :
     LinearIndependent R v ↔ ∀ g : ι → R, (∑ i, g i • v i) = 0 → ∀ i, g i = 0 :=
   by
@@ -169,6 +201,12 @@ theorem Fintype.linearIndependent_iff [Fintype ι] :
   rw [hg i hi, zero_smul]
 #align fintype.linear_independent_iff Fintype.linearIndependent_iff
 
+/- warning: fintype.linear_independent_iff' -> Fintype.linearIndependent_iff' is a dubious translation:
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(MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.module.{u2, u2, 0, max u1 u2, u3} R R Nat (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) (fun (_x : LinearEquiv.{0, 0, max u1 u2 u3, max (max u1 u2) u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (forall (i : ι), (fun (i : ι) => R) i) M (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5) (Pi.addCommMonoid.{u1, max u2 u3} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u1 u2, u3} R R (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u1, max u2 u3, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.module.{u2, u2, 0, u2, u3} R R Nat ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.module.{u2, u2, 0, max u1 u2, u3} R R Nat (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) => (forall (i : ι), LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) -> (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (forall (i : ι), (fun (i : ι) => R) i) M (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5)) (LinearEquiv.hasCoeToFun.{0, 0, max u1 u2 u3, max (max u1 u2) u3} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (forall (i : ι), (fun (i : ι) => R) i) M (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, max u2 u3} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u1 u2, u3} R R (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u1, max u2 u3, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (i : ι) => R) i) M ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u3} R R ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.module.{u2, u2, 0, u2, u3} R R Nat ((fun (i : ι) => R) i) M _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) _inst_2 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.module.{u2, u2, 0, max u1 u2, u3} R R Nat (forall (i : ι), (fun (i : ι) => R) i) M _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) _inst_2 (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)) (LinearMap.lsum.{u2, u3, u1, u2, 0} R M ι _inst_1 (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) Nat _inst_2 _inst_5 _inst_8 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u1} ι a b)) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M _inst_1 _inst_2 _inst_5))) (fun (i : ι) => LinearMap.smulRight.{u2, u2, u3, u2} R ((fun (i : ι) => R) i) M ((fun (i : ι) => R) i) _inst_1 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) _inst_5 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_1 ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i) _inst_5 (IsScalarTower.left.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2))) (Module.toMulActionWithZero.{u2, u3} R M _inst_1 _inst_2 _inst_5))) (LinearMap.id.{u2, u2} R ((fun (i : ι) => R) i) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) ((fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)) (v i)))) (Bot.bot.{max u1 u2} (Submodule.{u2, max u1 u2} R (forall (i : ι), (fun (i : ι) => R) i) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i))) (Submodule.hasBot.{u2, max u1 u2} R (forall (i : ι), (fun (i : ι) => R) i) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => (fun (i : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) i)))))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] [_inst_8 : Fintype.{u3} ι], Iff (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) (Eq.{max (succ u3) (succ u2)} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) (LinearMap.ker.{u2, u2, max u3 u2, u1, max (max u3 u2) u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun 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(Semiring.toModule.{u2} R _inst_1)) (v i))) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, max u3 u2, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (max (succ u2) (succ u3)) (succ u1), max (max (succ u2) (succ u3)) (succ u1)} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (_x : forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) => LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) _x) (SMulHomClass.toFunLike.{max (max u2 u3) u1, 0, max (max u2 u3) u1, max (max u2 u3) u1} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))))))) (SMulZeroClass.toSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toZero.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribSMul.toSMulZeroClass.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddMonoid.toAddZeroClass.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u1, 0, max (max u2 u3) u1, max (max u2 u3) u1} (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u2 u3) u1} (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (Module.toDistribMulAction.{0, max (max u2 u3) u1} Nat (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (SemilinearMapClass.distribMulActionHomClass.{0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max (max u2 u3) u1, max (max u2 u3) u1, max (max u2 u3) u1} Nat Nat (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (LinearEquiv.{0, 0, max (max u2 u1) u3, max u1 u2 u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (forall (i : ι), LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5) (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, max u2 u1} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) Nat Nat.semiring (fun (i : ι) => LinearMap.addCommMonoid.{u2, u2, u2, u1} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : ι) => LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u2, u1} R R Nat R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun 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ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5) (LinearMap.{u2, u2, max u2 u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) 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i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u1} R R (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) _inst_2 (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Pi.module.{u3, max u2 u1, 0} ι (fun (i : ι) => LinearMap.{u2, u2, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) _inst_2 (Semiring.toModule.{u2} R _inst_1) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, max u2 u3, u1} R R Nat (ι -> R) M _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun 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(Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (LinearMap.lsum.{u2, u1, u3, u2, 0} R M ι _inst_1 (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (i : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (i : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (i : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) Nat _inst_2 _inst_5 _inst_8 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u3} ι a b)) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (fun (i : ι) => LinearMap.smulRight.{u2, u2, u1, u2} R R M R _inst_1 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) _inst_5 (Semiring.toModule.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R _inst_1) _inst_5 (IsScalarTower.left.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_2 _inst_5))) (LinearMap.id.{u2, u2} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (v i)))) (Bot.bot.{max u3 u2} (Submodule.{u2, max u3 u2} R (ι -> R) _inst_1 (Pi.addCommMonoid.{u3, 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(fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1)))) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.1397 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align fintype.linear_independent_iff' Fintype.linearIndependent_iff'ₓ'. -/
 /-- A finite family of vectors `v i` is linear independent iff the linear map that sends
 `c : ι → R` to `∑ i, c i • v i` has the trivial kernel. -/
 theorem Fintype.linearIndependent_iff' [Fintype ι] :
@@ -177,15 +215,33 @@ theorem Fintype.linearIndependent_iff' [Fintype ι] :
   by simp [Fintype.linearIndependent_iff, LinearMap.ker_eq_bot', funext_iff] <;> skip
 #align fintype.linear_independent_iff' Fintype.linearIndependent_iff'
 
+/- warning: fintype.not_linear_independent_iff -> Fintype.not_linearIndependent_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fintype.not_linear_independent_iff Fintype.not_linearIndependent_iffₓ'. -/
 theorem Fintype.not_linearIndependent_iff [Fintype ι] :
     ¬LinearIndependent R v ↔ ∃ g : ι → R, (∑ i, g i • v i) = 0 ∧ ∃ i, g i ≠ 0 := by
   simpa using not_iff_not.2 Fintype.linearIndependent_iff
 #align fintype.not_linear_independent_iff Fintype.not_linearIndependent_iff
 
+/- warning: linear_independent_empty_type -> linearIndependent_empty_type is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align linear_independent_empty_type linearIndependent_empty_typeₓ'. -/
 theorem linearIndependent_empty_type [IsEmpty ι] : LinearIndependent R v :=
   linearIndependent_iff.mpr fun v hv => Subsingleton.elim v 0
 #align linear_independent_empty_type linearIndependent_empty_type
 
+/- warning: linear_independent.ne_zero -> LinearIndependent.ne_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_independent.ne_zero LinearIndependent.ne_zeroₓ'. -/
 theorem LinearIndependent.ne_zero [Nontrivial R] (i : ι) (hv : LinearIndependent R v) : v i ≠ 0 :=
   fun h =>
   zero_ne_one' R <|
@@ -197,6 +253,12 @@ theorem LinearIndependent.ne_zero [Nontrivial R] (i : ι) (hv : LinearIndependen
         · simp [h])
 #align linear_independent.ne_zero LinearIndependent.ne_zero
 
+/- warning: linear_independent.comp -> LinearIndependent.comp is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_independent.comp LinearIndependent.compₓ'. -/
 /-- A subfamily of a linearly independent family (i.e., a composition with an injective map) is a
 linearly independent family. -/
 theorem LinearIndependent.comp (h : LinearIndependent R v) (f : ι' → ι) (hf : Injective f) :
@@ -211,10 +273,22 @@ theorem LinearIndependent.comp (h : LinearIndependent R v) (f : ι' → ι) (hf
   rw [Finsupp.mapDomain_apply hf]
 #align linear_independent.comp LinearIndependent.comp
 
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+Case conversion may be inaccurate. Consider using '#align linear_independent.coe_range LinearIndependent.coe_rangeₓ'. -/
 theorem LinearIndependent.coe_range (i : LinearIndependent R v) :
     LinearIndependent R (coe : range v → M) := by simpa using i.comp _ (range_splitting_injective v)
 #align linear_independent.coe_range LinearIndependent.coe_range
 
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 /-- If `v` is a linearly independent family of vectors and the kernel of a linear map `f` is
 disjoint with the submodule spanned by the vectors of `v`, then `f ∘ v` is a linearly independent
 family of vectors. See also `linear_independent.map'` for a special case assuming `ker f = ⊥`. -/
@@ -232,6 +306,12 @@ theorem LinearIndependent.map (hv : LinearIndependent R v) {f : M →ₗ[R] M'}
   exact fun _ => rfl
 #align linear_independent.map LinearIndependent.map
 
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 /-- An injective linear map sends linearly independent families of vectors to linearly independent
 families of vectors. See also `linear_independent.map` for a more general statement. -/
 theorem LinearIndependent.map' (hv : LinearIndependent R v) (f : M →ₗ[R] M') (hf_inj : f.ker = ⊥) :
@@ -239,6 +319,12 @@ theorem LinearIndependent.map' (hv : LinearIndependent R v) (f : M →ₗ[R] M')
   hv.map <| by simp [hf_inj]
 #align linear_independent.map' LinearIndependent.map'
 
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 /-- If the image of a family of vectors under a linear map is linearly independent, then so is
 the original family. -/
 theorem LinearIndependent.of_comp (f : M →ₗ[R] M') (hfv : LinearIndependent R (f ∘ v)) :
@@ -249,6 +335,12 @@ theorem LinearIndependent.of_comp (f : M →ₗ[R] M') (hfv : LinearIndependent
     linearIndependent_iff'.1 hfv s g this i his
 #align linear_independent.of_comp LinearIndependent.of_comp
 
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 /-- If `f` is an injective linear map, then the family `f ∘ v` is linearly independent
 if and only if the family `v` is linearly independent. -/
 protected theorem LinearMap.linearIndependent_iff (f : M →ₗ[R] M') (hf_inj : f.ker = ⊥) :
@@ -256,41 +348,75 @@ protected theorem LinearMap.linearIndependent_iff (f : M →ₗ[R] M') (hf_inj :
   ⟨fun h => h.of_comp f, fun h => h.map <| by simp only [hf_inj, disjoint_bot_right]⟩
 #align linear_map.linear_independent_iff LinearMap.linearIndependent_iff
 
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 @[nontriviality]
 theorem linearIndependent_of_subsingleton [Subsingleton R] : LinearIndependent R v :=
   linearIndependent_iff.2 fun l hl => Subsingleton.elim _ _
 #align linear_independent_of_subsingleton linearIndependent_of_subsingleton
 
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 theorem linearIndependent_equiv (e : ι ≃ ι') {f : ι' → M} :
     LinearIndependent R (f ∘ e) ↔ LinearIndependent R f :=
   ⟨fun h => Function.comp.right_id f ▸ e.self_comp_symm ▸ h.comp _ e.symm.Injective, fun h =>
     h.comp _ e.Injective⟩
 #align linear_independent_equiv linearIndependent_equiv
 
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 theorem linearIndependent_equiv' (e : ι ≃ ι') {f : ι' → M} {g : ι → M} (h : f ∘ e = g) :
     LinearIndependent R g ↔ LinearIndependent R f :=
   h ▸ linearIndependent_equiv e
 #align linear_independent_equiv' linearIndependent_equiv'
 
+#print linearIndependent_subtype_range /-
 theorem linearIndependent_subtype_range {ι} {f : ι → M} (hf : Injective f) :
     LinearIndependent R (coe : range f → M) ↔ LinearIndependent R f :=
   Iff.symm <| linearIndependent_equiv' (Equiv.ofInjective f hf) rfl
 #align linear_independent_subtype_range linearIndependent_subtype_range
+-/
 
 alias linearIndependent_subtype_range ↔ LinearIndependent.of_subtype_range _
 #align linear_independent.of_subtype_range LinearIndependent.of_subtype_range
 
+#print linearIndependent_image /-
 theorem linearIndependent_image {ι} {s : Set ι} {f : ι → M} (hf : Set.InjOn f s) :
     (LinearIndependent R fun x : s => f x) ↔ LinearIndependent R fun x : f '' s => (x : M) :=
   linearIndependent_equiv' (Equiv.Set.imageOfInjOn _ _ hf) rfl
 #align linear_independent_image linearIndependent_image
+-/
 
+/- warning: linear_independent_span -> linearIndependent_span is a dubious translation:
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+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2], (LinearIndependent.{u1, u2, u3} ι R M v _inst_1 _inst_2 _inst_5) -> (LinearIndependent.{u1, u2, u3} ι R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u2, u3} R M _inst_1 _inst_2 _inst_5)) (Submodule.span.{u2, u3} R M _inst_1 _inst_2 _inst_5 (Set.range.{u3, succ u1} M ι v))) (fun (i : ι) => Subtype.mk.{succ u3} M (fun (x : M) => Membership.Mem.{u3, u3} M (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u2, u3} R M _inst_1 _inst_2 _inst_5)) x (Submodule.span.{u2, u3} R M _inst_1 _inst_2 _inst_5 (Set.range.{u3, succ u1} M ι v))) (v i) (Submodule.subset_span.{u2, u3} R M _inst_1 _inst_2 _inst_5 (Set.range.{u3, succ u1} M ι v) (v i) (Set.mem_range_self.{u3, succ u1} M ι v i))) _inst_1 (Submodule.addCommMonoid.{u2, u3} R M _inst_1 _inst_2 _inst_5 (Submodule.span.{u2, u3} R M _inst_1 _inst_2 _inst_5 (Set.range.{u3, succ u1} M ι v))) (Submodule.module.{u2, u3} R M _inst_1 _inst_2 _inst_5 (Submodule.span.{u2, u3} R M _inst_1 _inst_2 _inst_5 (Set.range.{u3, succ u1} M ι v))))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2], (LinearIndependent.{u3, u2, u1} ι R M v _inst_1 _inst_2 _inst_5) -> (LinearIndependent.{u3, u2, u1} ι R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) x (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, succ u3} M ι v)))) (fun (i : ι) => Subtype.mk.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) x (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, succ u3} M ι v))) (v i) (Submodule.subset_span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, succ u3} M ι v) (v i) (Set.mem_range_self.{succ u3, u1} M ι v i))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, succ u3} M ι v))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, succ u3} M ι v))))
+Case conversion may be inaccurate. Consider using '#align linear_independent_span linearIndependent_spanₓ'. -/
 theorem linearIndependent_span (hs : LinearIndependent R v) :
     @LinearIndependent ι R (span R (range v)) (fun i : ι => ⟨v i, subset_span (mem_range_self i)⟩) _
       _ _ :=
   LinearIndependent.of_comp (span R (range v)).Subtype hs
 #align linear_independent_span linearIndependent_span
 
+/- warning: linear_independent.fin_cons' -> LinearIndependent.fin_cons' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {m : Nat} (x : M) (v : (Fin m) -> M), (LinearIndependent.{0, u1, u2} (Fin m) R M v _inst_1 _inst_2 _inst_5) -> (forall (c : R) (y : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_5 (Set.range.{u2, 1} M (Fin m) v))), (Eq.{succ u2} M (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) (SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_5)))) c x) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_5 (Set.range.{u2, 1} M (Fin m) v))) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_5 (Set.range.{u2, 1} M (Fin m) v))) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_5 (Set.range.{u2, 1} M (Fin m) v))) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_5 (Set.range.{u2, 1} M (Fin m) v))) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_5)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_5 (Set.range.{u2, 1} M (Fin m) v))))))) y)) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))))) -> (Eq.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) -> (LinearIndependent.{0, u1, u2} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R M (Fin.cons.{u2} m (fun (ᾰ : Fin (Nat.succ m)) => M) x v) _inst_1 _inst_2 _inst_5)
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {m : Nat} (x : M) (v : (Fin m) -> M), (LinearIndependent.{0, u2, u1} (Fin m) R M v _inst_1 _inst_2 _inst_5) -> (forall (c : R) (y : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) x (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, 1} M (Fin m) v)))), (Eq.{succ u1} M (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)))) (HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) c x) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_5 (Set.range.{u1, 1} M (Fin m) v)))) y)) (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))) -> (Eq.{succ u2} R c (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))) -> (LinearIndependent.{0, u2, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R M (Fin.cons.{u1} m (fun (ᾰ : Fin (Nat.succ m)) => M) x v) _inst_1 _inst_2 _inst_5)
+Case conversion may be inaccurate. Consider using '#align linear_independent.fin_cons' LinearIndependent.fin_cons'ₓ'. -/
 /-- See `linear_independent.fin_cons` for a family of elements in a vector space. -/
 theorem LinearIndependent.fin_cons' {m : ℕ} (x : M) (v : Fin m → M) (hli : LinearIndependent R v)
     (x_ortho : ∀ (c : R) (y : Submodule.span R (Set.range v)), c • x + y = (0 : M) → c = 0) :
@@ -307,6 +433,12 @@ theorem LinearIndependent.fin_cons' {m : ℕ} (x : M) (v : Fin m → M) (hli : L
   exact Fin.cases this (hli _ total_eq) j
 #align linear_independent.fin_cons' LinearIndependent.fin_cons'
 
+/- warning: linear_independent.restrict_scalars -> LinearIndependent.restrict_scalars is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {ι : Type.{u4}} {R : Type.{u2}} {K : Type.{u3}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] [_inst_8 : Semiring.{u3} K] [_inst_9 : SMulWithZero.{u2, u3} R K (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toZero.{u3} K (Semiring.toMonoidWithZero.{u3} K _inst_8))] [_inst_10 : Module.{u3, u1} K M _inst_8 _inst_2] [_inst_11 : IsScalarTower.{u2, u3, u1} R K M (SMulZeroClass.toSMul.{u2, u3} R K (MonoidWithZero.toZero.{u3} K (Semiring.toMonoidWithZero.{u3} K _inst_8)) (SMulWithZero.toSMulZeroClass.{u2, u3} R K (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toZero.{u3} K (Semiring.toMonoidWithZero.{u3} K _inst_8)) _inst_9)) (SMulZeroClass.toSMul.{u3, u1} K M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u1} K M (MonoidWithZero.toZero.{u3} K (Semiring.toMonoidWithZero.{u3} K _inst_8)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u1} K M (Semiring.toMonoidWithZero.{u3} K _inst_8) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u3, u1} K M _inst_8 _inst_2 _inst_10)))) (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M _inst_1 _inst_2 _inst_5))))], (Function.Injective.{succ u2, succ u3} R K (fun (r : R) => HSMul.hSMul.{u2, u3, u3} R K K (instHSMul.{u2, u3} R K (SMulZeroClass.toSMul.{u2, u3} R K (MonoidWithZero.toZero.{u3} K (Semiring.toMonoidWithZero.{u3} K _inst_8)) (SMulWithZero.toSMulZeroClass.{u2, u3} R K (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toZero.{u3} K (Semiring.toMonoidWithZero.{u3} K _inst_8)) _inst_9))) r (OfNat.ofNat.{u3} K 1 (One.toOfNat1.{u3} K (Semiring.toOne.{u3} K _inst_8))))) -> (LinearIndependent.{u4, u3, u1} ι K M v _inst_8 _inst_2 _inst_10) -> (LinearIndependent.{u4, u2, u1} ι R M v _inst_1 _inst_2 _inst_5)
+Case conversion may be inaccurate. Consider using '#align linear_independent.restrict_scalars LinearIndependent.restrict_scalarsₓ'. -/
 /-- A set of linearly independent vectors in a module `M` over a semiring `K` is also linearly
 independent over a subring `R` of `K`.
 The implementation uses minimal assumptions about the relationship between `R`, `K` and `M`.
@@ -322,6 +454,7 @@ theorem LinearIndependent.restrict_scalars [Semiring K] [SMulWithZero R K] [Modu
   exact hg
 #align linear_independent.restrict_scalars LinearIndependent.restrict_scalars
 
+#print linearIndependent_finset_map_embedding_subtype /-
 /-- Every finite subset of a linearly independent set is linearly independent. -/
 theorem linearIndependent_finset_map_embedding_subtype (s : Set M)
     (li : LinearIndependent R (coe : s → M)) (t : Finset s) :
@@ -340,7 +473,14 @@ theorem linearIndependent_finset_map_embedding_subtype (s : Set M)
   obtain ⟨b, hb, rfl⟩ := hy
   simp only [imp_self, Subtype.mk_eq_mk]
 #align linear_independent_finset_map_embedding_subtype linearIndependent_finset_map_embedding_subtype
+-/
 
+/- warning: linear_independent_bounded_of_finset_linear_independent_bounded -> linearIndependent_bounded_of_finset_linearIndependent_bounded is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {n : Nat}, (forall (s : Finset.{u2} M), (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Finset.{u2} M) Type.{u2} (Finset.hasCoeToSort.{u2} M) s) R M (fun (i : coeSort.{succ u2, succ (succ u2)} (Finset.{u2} M) Type.{u2} (Finset.hasCoeToSort.{u2} M) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Finset.{u2} M) Type.{u2} (Finset.hasCoeToSort.{u2} M) s) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Finset.{u2} M) Type.{u2} (Finset.hasCoeToSort.{u2} M) s) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Finset.{u2} M) Type.{u2} (Finset.hasCoeToSort.{u2} M) s) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Finset.{u2} M) Type.{u2} (Finset.hasCoeToSort.{u2} M) s) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Finset.{u2} M) (Finset.hasMem.{u2} M) x s))))) i) _inst_1 _inst_2 _inst_5) -> (LE.le.{0} Nat Nat.hasLe (Finset.card.{u2} M s) n)) -> (forall (s : Set.{u2} M), (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x s)))))) _inst_1 _inst_2 _inst_5) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} (Cardinal.mk.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s)) ((fun (a : Type) (b : Type.{succ u2}) [self : HasLiftT.{1, succ (succ u2)} a b] => self.0) Nat Cardinal.{u2} (HasLiftT.mk.{1, succ (succ u2)} Nat Cardinal.{u2} (CoeTCₓ.coe.{1, succ (succ u2)} Nat Cardinal.{u2} (Nat.castCoe.{succ u2} Cardinal.{u2} Cardinal.hasNatCast.{u2}))) n)))
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_2] {n : Nat}, (forall (s : Finset.{u2} M), (LinearIndependent.{u2, u1, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Finset.{u2} M) (Finset.instMembershipFinset.{u2} M) x s)) R M (fun (i : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Finset.{u2} M) (Finset.instMembershipFinset.{u2} M) x s)) => Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Finset.{u2} M) (Finset.instMembershipFinset.{u2} M) x s) i) _inst_1 _inst_2 _inst_5) -> (LE.le.{0} Nat instLENat (Finset.card.{u2} M s) n)) -> (forall (s : Set.{u2} M), (LinearIndependent.{u2, u1, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s)) R M (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s)) _inst_1 _inst_2 _inst_5) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Cardinal.mk.{u2} (Set.Elem.{u2} M s)) (Nat.cast.{succ u2} Cardinal.{u2} Cardinal.instNatCastCardinal.{u2} n)))
+Case conversion may be inaccurate. Consider using '#align linear_independent_bounded_of_finset_linear_independent_bounded linearIndependent_bounded_of_finset_linearIndependent_boundedₓ'. -/
 /-- If every finite set of linearly independent vectors has cardinality at most `n`,
 then the same is true for arbitrary sets of linearly independent vectors.
 -/
@@ -361,6 +501,12 @@ section Subtype
 /-! The following lemmas use the subtype defined by a set in `M` as the index set `ι`. -/
 
 
+/- warning: linear_independent_comp_subtype -> linearIndependent_comp_subtype is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_independent_comp_subtype linearIndependent_comp_subtypeₓ'. -/
 theorem linearIndependent_comp_subtype {s : Set ι} :
     LinearIndependent R (v ∘ coe : s → M) ↔
       ∀ l ∈ Finsupp.supported R R s, (Finsupp.total ι M R v) l = 0 → l = 0 :=
@@ -380,37 +526,73 @@ theorem linearIndependent_comp_subtype {s : Set ι} :
       exacts[fun _ => zero_smul _ _, fun _ _ _ => add_smul _ _ _]
 #align linear_independent_comp_subtype linearIndependent_comp_subtype
 
-theorem linear_dependent_comp_subtype' {s : Set ι} :
+/- warning: linear_dependent_comp_subtype' -> linearDependent_comp_subtype' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align linear_dependent_comp_subtype' linearDependent_comp_subtype'ₓ'. -/
+theorem linearDependent_comp_subtype' {s : Set ι} :
     ¬LinearIndependent R (v ∘ coe : s → M) ↔
       ∃ f : ι →₀ R, f ∈ Finsupp.supported R R s ∧ Finsupp.total ι M R v f = 0 ∧ f ≠ 0 :=
   by simp [linearIndependent_comp_subtype]
-#align linear_dependent_comp_subtype' linear_dependent_comp_subtype'
-
+#align linear_dependent_comp_subtype' linearDependent_comp_subtype'
+
+/- warning: linear_dependent_comp_subtype -> linearDependent_comp_subtype is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align linear_dependent_comp_subtype linearDependent_comp_subtypeₓ'. -/
 /-- A version of `linear_dependent_comp_subtype'` with `finsupp.total` unfolded. -/
-theorem linear_dependent_comp_subtype {s : Set ι} :
+theorem linearDependent_comp_subtype {s : Set ι} :
     ¬LinearIndependent R (v ∘ coe : s → M) ↔
       ∃ f : ι →₀ R, f ∈ Finsupp.supported R R s ∧ (∑ i in f.support, f i • v i) = 0 ∧ f ≠ 0 :=
-  linear_dependent_comp_subtype'
-#align linear_dependent_comp_subtype linear_dependent_comp_subtype
-
+  linearDependent_comp_subtype'
+#align linear_dependent_comp_subtype linearDependent_comp_subtype
+
+/- warning: linear_independent_subtype -> linearIndependent_subtype is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align linear_independent_subtype linearIndependent_subtypeₓ'. -/
 theorem linearIndependent_subtype {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
       ∀ l ∈ Finsupp.supported R R s, (Finsupp.total M M R id) l = 0 → l = 0 :=
   by apply @linearIndependent_comp_subtype _ _ _ id
 #align linear_independent_subtype linearIndependent_subtype
 
+/- warning: linear_independent_comp_subtype_disjoint -> linearIndependent_comp_subtype_disjoint is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align linear_independent_comp_subtype_disjoint linearIndependent_comp_subtype_disjointₓ'. -/
 theorem linearIndependent_comp_subtype_disjoint {s : Set ι} :
     LinearIndependent R (v ∘ coe : s → M) ↔
       Disjoint (Finsupp.supported R R s) (Finsupp.total ι M R v).ker :=
   by rw [linearIndependent_comp_subtype, LinearMap.disjoint_ker]
 #align linear_independent_comp_subtype_disjoint linearIndependent_comp_subtype_disjoint
 
+/- warning: linear_independent_subtype_disjoint -> linearIndependent_subtype_disjoint is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align linear_independent_subtype_disjoint linearIndependent_subtype_disjointₓ'. -/
 theorem linearIndependent_subtype_disjoint {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
       Disjoint (Finsupp.supported R R s) (Finsupp.total M M R id).ker :=
   by apply @linearIndependent_comp_subtype_disjoint _ _ _ id
 #align linear_independent_subtype_disjoint linearIndependent_subtype_disjoint
 
+/- warning: linear_independent_iff_total_on -> linearIndependent_iff_totalOn is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align linear_independent_iff_total_on linearIndependent_iff_totalOnₓ'. -/
 theorem linearIndependent_iff_totalOn {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔ (Finsupp.totalOn M M R id s).ker = ⊥ := by
   rw [Finsupp.totalOn, LinearMap.ker, LinearMap.comap_codRestrict, map_bot, comap_bot,
@@ -418,6 +600,12 @@ theorem linearIndependent_iff_totalOn {s : Set M} :
     map_comap_subtype, map_le_iff_le_comap, comap_bot, ker_subtype, le_bot_iff]
 #align linear_independent_iff_total_on linearIndependent_iff_totalOn
 
+/- warning: linear_independent.restrict_of_comp_subtype -> LinearIndependent.restrict_of_comp_subtype is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_1 _inst_2] {s : Set.{u1} ι}, (LinearIndependent.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) R M (Function.comp.{succ u1, succ u1, succ u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι M v ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeSubtype.{succ u1} ι (fun (x : ι) => Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) x s))))))) _inst_1 _inst_2 _inst_5) -> (LinearIndependent.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) R M (Set.restrict.{u1, u3} ι (fun (ᾰ : ι) => M) s v) _inst_1 _inst_2 _inst_5)
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u3} ι}, (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι M v (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5) -> (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (Set.restrict.{u3, u1} ι (fun (ᾰ : ι) => M) s v) _inst_1 _inst_2 _inst_5)
+Case conversion may be inaccurate. Consider using '#align linear_independent.restrict_of_comp_subtype LinearIndependent.restrict_of_comp_subtypeₓ'. -/
 theorem LinearIndependent.restrict_of_comp_subtype {s : Set ι}
     (hs : LinearIndependent R (v ∘ coe : s → M)) : LinearIndependent R (s.restrict v) :=
   hs
@@ -425,27 +613,34 @@ theorem LinearIndependent.restrict_of_comp_subtype {s : Set ι}
 
 variable (R M)
 
+#print linearIndependent_empty /-
 theorem linearIndependent_empty : LinearIndependent R (fun x => x : (∅ : Set M) → M) := by
   simp [linearIndependent_subtype_disjoint]
 #align linear_independent_empty linearIndependent_empty
+-/
 
 variable {R M}
 
+#print LinearIndependent.mono /-
 theorem LinearIndependent.mono {t s : Set M} (h : t ⊆ s) :
     LinearIndependent R (fun x => x : s → M) → LinearIndependent R (fun x => x : t → M) :=
   by
   simp only [linearIndependent_subtype_disjoint]
   exact Disjoint.mono_left (Finsupp.supported_mono h)
 #align linear_independent.mono LinearIndependent.mono
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+#print linearIndependent_of_finite /-
 theorem linearIndependent_of_finite (s : Set M)
     (H : ∀ (t) (_ : t ⊆ s), Set.Finite t → LinearIndependent R (fun x => x : t → M)) :
     LinearIndependent R (fun x => x : s → M) :=
   linearIndependent_subtype.2 fun l hl =>
     linearIndependent_subtype.1 (H _ hl (Finset.finite_toSet _)) l (Subset.refl _)
 #align linear_independent_of_finite linearIndependent_of_finite
+-/
 
+#print linearIndependent_unionᵢ_of_directed /-
 theorem linearIndependent_unionᵢ_of_directed {η : Type _} {s : η → Set M} (hs : Directed (· ⊆ ·) s)
     (h : ∀ i, LinearIndependent R (fun x => x : s i → M)) :
     LinearIndependent R (fun x => x : (⋃ i, s i) → M) :=
@@ -460,21 +655,26 @@ theorem linearIndependent_unionᵢ_of_directed {η : Type _} {s : η → Set M}
     rintro _ ⟨_, ⟨i, _⟩, _⟩
     exact hη ⟨i⟩
 #align linear_independent_Union_of_directed linearIndependent_unionᵢ_of_directed
+-/
 
+#print linearIndependent_unionₛ_of_directed /-
 theorem linearIndependent_unionₛ_of_directed {s : Set (Set M)} (hs : DirectedOn (· ⊆ ·) s)
     (h : ∀ a ∈ s, LinearIndependent R (fun x => x : (a : Set M) → M)) :
     LinearIndependent R (fun x => x : ⋃₀ s → M) := by
   rw [sUnion_eq_Union] <;>
     exact linearIndependent_unionᵢ_of_directed hs.directed_coe (by simpa using h)
 #align linear_independent_sUnion_of_directed linearIndependent_unionₛ_of_directed
+-/
 
-theorem linearIndependent_bUnion_of_directed {η} {s : Set η} {t : η → Set M}
+#print linearIndependent_bunionᵢ_of_directed /-
+theorem linearIndependent_bunionᵢ_of_directed {η} {s : Set η} {t : η → Set M}
     (hs : DirectedOn (t ⁻¹'o (· ⊆ ·)) s) (h : ∀ a ∈ s, LinearIndependent R (fun x => x : t a → M)) :
     LinearIndependent R (fun x => x : (⋃ a ∈ s, t a) → M) := by
   rw [bUnion_eq_Union] <;>
     exact
       linearIndependent_unionᵢ_of_directed (directed_comp.2 <| hs.directed_coe) (by simpa using h)
-#align linear_independent_bUnion_of_directed linearIndependent_bUnion_of_directed
+#align linear_independent_bUnion_of_directed linearIndependent_bunionᵢ_of_directed
+-/
 
 end Subtype
 
@@ -493,15 +693,33 @@ variable [Module R M] [Module R M'] [Module R M'']
 
 variable {a b : R} {x y : M}
 
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+Case conversion may be inaccurate. Consider using '#align linear_independent_iff_injective_total linearIndependent_iff_injective_totalₓ'. -/
 theorem linearIndependent_iff_injective_total :
     LinearIndependent R v ↔ Function.Injective (Finsupp.total ι M R v) :=
   linearIndependent_iff.trans
     (injective_iff_map_eq_zero (Finsupp.total ι M R v).toAddMonoidHom).symm
 #align linear_independent_iff_injective_total linearIndependent_iff_injective_total
 
+/- warning: linear_independent.injective_total -> LinearIndependent.injective_total is a dubious translation:
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 alias linearIndependent_iff_injective_total ↔ LinearIndependent.injective_total _
 #align linear_independent.injective_total LinearIndependent.injective_total
 
+/- warning: linear_independent.injective -> LinearIndependent.injective is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_independent.injective LinearIndependent.injectiveₓ'. -/
 theorem LinearIndependent.injective [Nontrivial R] (hv : LinearIndependent R v) : Injective v :=
   by
   intro i j hij
@@ -517,6 +735,12 @@ theorem LinearIndependent.injective [Nontrivial R] (hv : LinearIndependent R v)
   simpa [Finsupp.single_eq_single_iff] using h_single_eq
 #align linear_independent.injective LinearIndependent.injective
 
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 theorem LinearIndependent.to_subtype_range {ι} {f : ι → M} (hf : LinearIndependent R f) :
     LinearIndependent R (coe : range f → M) :=
   by
@@ -524,11 +748,23 @@ theorem LinearIndependent.to_subtype_range {ι} {f : ι → M} (hf : LinearIndep
   exact (linearIndependent_subtype_range hf.injective).2 hf
 #align linear_independent.to_subtype_range LinearIndependent.to_subtype_range
 
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 theorem LinearIndependent.to_subtype_range' {ι} {f : ι → M} (hf : LinearIndependent R f) {t}
     (ht : range f = t) : LinearIndependent R (coe : t → M) :=
   ht ▸ hf.to_subtype_range
 #align linear_independent.to_subtype_range' LinearIndependent.to_subtype_range'
 
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+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u4}} {ι' : Type.{u3}} (s : Set.{u4} ι) (f : ι -> ι') (g : ι' -> M), (LinearIndependent.{u4, u2, u1} (Set.Elem.{u4} ι s) R M (fun (x : Set.Elem.{u4} ι s) => g (f (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) x))) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι' (Set.image.{u4, u3} ι ι' f s)) R M (fun (x : Set.Elem.{u3} ι' (Set.image.{u4, u3} ι ι' f s)) => g (Subtype.val.{succ u3} ι' (fun (x : ι') => Membership.mem.{u3, u3} ι' (Set.{u3} ι') (Set.instMembershipSet.{u3} ι') x (Set.image.{u4, u3} ι ι' f s)) x)) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
+Case conversion may be inaccurate. Consider using '#align linear_independent.image_of_comp LinearIndependent.image_of_compₓ'. -/
 theorem LinearIndependent.image_of_comp {ι ι'} (s : Set ι) (f : ι → ι') (g : ι' → M)
     (hs : LinearIndependent R fun x : s => g (f x)) : LinearIndependent R fun x : f '' s => g x :=
   by
@@ -537,11 +773,23 @@ theorem LinearIndependent.image_of_comp {ι ι'} (s : Set ι) (f : ι → ι') (
   exact (linearIndependent_equiv' (Equiv.Set.imageOfInjOn f s this) rfl).1 hs
 #align linear_independent.image_of_comp LinearIndependent.image_of_comp
 
+/- warning: linear_independent.image -> LinearIndependent.image is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} {s : Set.{u3} ι} {f : ι -> M}, (LinearIndependent.{u3, u1, u2} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) R M (fun (x : coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) => f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (coeSubtype.{succ u3} ι (fun (x : ι) => Membership.Mem.{u3, u3} ι (Set.{u3} ι) (Set.hasMem.{u3} ι) x s))))) x)) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.image.{u3, u2} ι M f s)) R M (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.image.{u3, u2} ι M f s)) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.image.{u3, u2} ι M f s)) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.image.{u3, u2} ι M f s)) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.image.{u3, u2} ι M f s)) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) (Set.image.{u3, u2} ι M f s)) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x (Set.image.{u3, u2} ι M f s)))))) x) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} {s : Set.{u3} ι} {f : ι -> M}, (LinearIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R M (fun (x : Set.Elem.{u3} ι s) => f (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s) x)) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (LinearIndependent.{u1, u2, u1} (Set.Elem.{u1} M (Set.image.{u3, u1} ι M f s)) R M (fun (x : Set.Elem.{u1} M (Set.image.{u3, u1} ι M f s)) => Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (Set.image.{u3, u1} ι M f s)) x) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
+Case conversion may be inaccurate. Consider using '#align linear_independent.image LinearIndependent.imageₓ'. -/
 theorem LinearIndependent.image {ι} {s : Set ι} {f : ι → M}
     (hs : LinearIndependent R fun x : s => f x) : LinearIndependent R fun x : f '' s => (x : M) :=
   by convert LinearIndependent.image_of_comp s f id hs
 #align linear_independent.image LinearIndependent.image
 
+/- warning: linear_independent.group_smul -> LinearIndependent.group_smul is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {G : Type.{u4}} [hG : Group.{u4} G] [_inst_8 : DistribMulAction.{u4, u2} G R (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (NonAssocRing.toAddGroupWithOne.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))] [_inst_9 : DistribMulAction.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))] [_inst_10 : IsScalarTower.{u4, u2, u3} G R M (SMulZeroClass.toHasSmul.{u4, u2} G R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (NonAssocRing.toAddGroupWithOne.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (DistribSMul.toSmulZeroClass.{u4, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (NonAssocRing.toAddGroupWithOne.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (DistribMulAction.toDistribSMul.{u4, u2} G R (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (NonAssocRing.toAddGroupWithOne.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) _inst_8))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)))) (SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u4, u2, u3} G R M (SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u1, u2, u3} ι R M (SMul.smul.{max u1 u4, max u1 u3} (ι -> G) (ι -> M) (Pi.smul'.{u1, u4, u3} ι (fun (ᾰ : ι) => G) (fun (ᾰ : ι) => M) (fun (i : ι) => SMulZeroClass.toHasSmul.{u4, u3} G M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))))) (DistribSMul.toSmulZeroClass.{u4, u3} G M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2)))) (DistribMulAction.toDistribSMul.{u4, u3} G M (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G hG)) (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_2))) _inst_9)))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)
+but is expected to have type
+  forall {ι : Type.{u4}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {G : Type.{u3}} [hG : Group.{u3} G] [_inst_8 : DistribMulAction.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))] [_inst_9 : DistribMulAction.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))] [_inst_10 : IsScalarTower.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u2} G R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (DistribSMul.toSMulZeroClass.{u3, u2} G R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))) (DistribMulAction.toDistribSMul.{u3, u2} G R (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1))) _inst_8))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9)))] [_inst_11 : SMulCommClass.{u3, u2, u1} G R M (SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))] {v : ι -> M}, (LinearIndependent.{u4, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> G), LinearIndependent.{u4, u2, u1} ι R M (HSMul.hSMul.{max u4 u3, max u4 u1, max u4 u1} (ι -> G) (ι -> M) (ι -> M) (instHSMul.{max u4 u3, max u4 u1} (ι -> G) (ι -> M) (Pi.smul'.{u4, u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6559 : ι) => G) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6553 : ι) => M) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u1} G M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (DistribSMul.toSMulZeroClass.{u3, u1} G M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2)))) (DistribMulAction.toDistribSMul.{u3, u1} G M (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G hG)) (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_2))) _inst_9))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
+Case conversion may be inaccurate. Consider using '#align linear_independent.group_smul LinearIndependent.group_smulₓ'. -/
 theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulAction G R]
     [DistribMulAction G M] [IsScalarTower G R M] [SMulCommClass G R M] {v : ι → M}
     (hv : LinearIndependent R v) (w : ι → G) : LinearIndependent R (w • v) :=
@@ -557,6 +805,12 @@ theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulActi
     erw [Pi.smul_apply, smul_assoc, smul_comm]
 #align linear_independent.group_smul LinearIndependent.group_smul
 
+/- warning: linear_independent.units_smul -> LinearIndependent.units_smul is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {v : ι -> M}, (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall (w : ι -> (Units.{u2} R (Ring.toMonoid.{u2} R _inst_1))), LinearIndependent.{u1, u2, u3} ι R M (SMul.smul.{max u1 u2, max u1 u3} (ι -> (Units.{u2} R (Ring.toMonoid.{u2} R _inst_1))) (ι -> M) (Pi.smul'.{u1, u2, u3} ι (fun (ᾰ : ι) => Units.{u2} R (Ring.toMonoid.{u2} R _inst_1)) (fun (ᾰ : ι) => M) (fun (i : ι) => Units.hasSmul.{u2, u3} R M (Ring.toMonoid.{u2} R _inst_1) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {v : ι -> M}, (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (w : ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))), LinearIndependent.{u3, u2, u1} ι R M (HSMul.hSMul.{max u3 u2, max u3 u1, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (ι -> M) (instHSMul.{max u3 u2, max u3 u1} (ι -> (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (ι -> M) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6789 : ι) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (fun (a._@.Mathlib.LinearAlgebra.LinearIndependent._hyg.6783 : ι) => M) (fun (i : ι) => Units.instSMulUnits.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))))) w v) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
+Case conversion may be inaccurate. Consider using '#align linear_independent.units_smul LinearIndependent.units_smulₓ'. -/
 -- This lemma cannot be proved with `linear_independent.group_smul` since the action of
 -- `Rˣ` on `R` is not commutative.
 theorem LinearIndependent.units_smul {v : ι → M} (hv : LinearIndependent R v) (w : ι → Rˣ) :
@@ -578,6 +832,7 @@ section Maximal
 
 universe v w
 
+#print LinearIndependent.Maximal /-
 /--
 A linearly independent family is maximal if there is no strictly larger linearly independent family.
 -/
@@ -586,7 +841,9 @@ def LinearIndependent.Maximal {ι : Type w} {R : Type u} [Semiring R] {M : Type
     [Module R M] {v : ι → M} (i : LinearIndependent R v) : Prop :=
   ∀ (s : Set M) (i' : LinearIndependent R (coe : s → M)) (h : range v ≤ s), range v = s
 #align linear_independent.maximal LinearIndependent.Maximal
+-/
 
+#print LinearIndependent.maximal_iff /-
 /-- An alternative characterization of a maximal linearly independent family,
 quantifying over types (in the same universe as `M`) into which the indexing family injects.
 -/
@@ -612,9 +869,16 @@ theorem LinearIndependent.maximal_iff {ι : Type w} {R : Type u} [Ring R] [Nontr
     rw [← image_univ, image_image] at q
     simpa using q
 #align linear_independent.maximal_iff LinearIndependent.maximal_iff
+-/
 
 end Maximal
 
+/- warning: linear_independent.eq_of_smul_apply_eq_smul_apply -> LinearIndependent.eq_of_smul_apply_eq_smul_apply is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {M : Type.{u3}} [_inst_8 : AddCommGroup.{u3} M] [_inst_9 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_8)] {v : ι -> M}, (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_8) _inst_9) -> (forall (c : R) (d : R) (i : ι) (j : ι), (Ne.{succ u2} R c (OfNat.ofNat.{u2} R 0 (OfNat.mk.{u2} R 0 (Zero.zero.{u2} R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))))))) -> (Eq.{succ u3} M (SMul.smul.{u2, u3} R M (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_8)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_8)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_8)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_8) _inst_9)))) c (v i)) (SMul.smul.{u2, u3} R M (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_8)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_8)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_8)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_8) _inst_9)))) d (v j))) -> (Eq.{succ u1} ι i j))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_8 : AddCommGroup.{u2} M] [_inst_9 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8)] {v : ι -> M}, (LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) -> (forall (c : R) (d : R) (i : ι) (j : ι), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) -> (Eq.{succ u2} M (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_8))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_8))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_8))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9))))) c (v i)) (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_8))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_8))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_8))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9))))) d (v j))) -> (Eq.{succ u3} ι i j))
+Case conversion may be inaccurate. Consider using '#align linear_independent.eq_of_smul_apply_eq_smul_apply LinearIndependent.eq_of_smul_apply_eq_smul_applyₓ'. -/
 /-- Linear independent families are injective, even if you multiply either side. -/
 theorem LinearIndependent.eq_of_smul_apply_eq_smul_apply {M : Type _} [AddCommGroup M] [Module R M]
     {v : ι → M} (li : LinearIndependent R v) (c d : R) (i j : ι) (hc : c ≠ 0)
@@ -639,6 +903,12 @@ section Subtype
 /-! The following lemmas use the subtype defined by a set in `M` as the index set `ι`. -/
 
 
+/- warning: linear_independent.disjoint_span_image -> LinearIndependent.disjoint_span_image is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall {s : Set.{u1} ι} {t : Set.{u1} ι}, (Disjoint.{u1} (Set.{u1} ι) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} ι) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} ι) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} ι) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} ι) (Set.completeBooleanAlgebra.{u1} ι)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} ι) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} ι) (Set.booleanAlgebra.{u1} ι))) s t) -> (Disjoint.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.partialOrder.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.orderBot.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.image.{u1, u3} ι M v s)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.image.{u1, u3} ι M v t))))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall {s : Set.{u3} ι} {t : 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)))))) s t) -> (Disjoint.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.image.{u3, u1} ι M v s)) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.image.{u3, u1} ι M v t))))
+Case conversion may be inaccurate. Consider using '#align linear_independent.disjoint_span_image LinearIndependent.disjoint_span_imageₓ'. -/
 theorem LinearIndependent.disjoint_span_image (hv : LinearIndependent R v) {s t : Set ι}
     (hs : Disjoint s t) : Disjoint (Submodule.span R <| v '' s) (Submodule.span R <| v '' t) :=
   by
@@ -649,6 +919,12 @@ theorem LinearIndependent.disjoint_span_image (hv : LinearIndependent R v) {s t
   simp [this]
 #align linear_independent.disjoint_span_image LinearIndependent.disjoint_span_image
 
+/- warning: linear_independent.not_mem_span_image -> LinearIndependent.not_mem_span_image is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_8 : Nontrivial.{u2} R], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (forall {s : Set.{u1} ι} {x : ι}, (Not (Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) x s)) -> (Not (Membership.Mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (v x) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.image.{u1, u3} ι M v s)))))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Nontrivial.{u2} R], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall {s : Set.{u3} ι} {x : ι}, (Not (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s)) -> (Not (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)) (v x) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.image.{u3, u1} ι M v s)))))
+Case conversion may be inaccurate. Consider using '#align linear_independent.not_mem_span_image LinearIndependent.not_mem_span_imageₓ'. -/
 theorem LinearIndependent.not_mem_span_image [Nontrivial R] (hv : LinearIndependent R v) {s : Set ι}
     {x : ι} (h : x ∉ s) : v x ∉ Submodule.span R (v '' s) :=
   by
@@ -662,6 +938,12 @@ theorem LinearIndependent.not_mem_span_image [Nontrivial R] (hv : LinearIndepend
   simpa using h
 #align linear_independent.not_mem_span_image LinearIndependent.not_mem_span_image
 
+/- warning: linear_independent.total_ne_of_not_mem_support -> LinearIndependent.total_ne_of_not_mem_support is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align linear_independent.total_ne_of_not_mem_support LinearIndependent.total_ne_of_not_mem_supportₓ'. -/
 theorem LinearIndependent.total_ne_of_not_mem_support [Nontrivial R] (hv : LinearIndependent R v)
     {x : ι} (f : ι →₀ R) (h : x ∉ f.support) : Finsupp.total ι M R v f ≠ v x :=
   by
@@ -674,6 +956,12 @@ theorem LinearIndependent.total_ne_of_not_mem_support [Nontrivial R] (hv : Linea
   exact p f (f.mem_supported_support R) rfl
 #align linear_independent.total_ne_of_not_mem_support LinearIndependent.total_ne_of_not_mem_support
 
+/- warning: linear_independent_sum -> linearIndependent_sum is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align linear_independent_sum linearIndependent_sumₓ'. -/
 theorem linearIndependent_sum {v : Sum ι ι' → M} :
     LinearIndependent R v ↔
       LinearIndependent R (v ∘ Sum.inl) ∧
@@ -709,6 +997,12 @@ theorem linearIndependent_sum {v : Sum ι ι' → M} :
     · exact smul_mem _ _ (subset_span ⟨Sum.inr i, mem_range_self _, rfl⟩)
 #align linear_independent_sum linearIndependent_sum
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align linear_independent.sum_type LinearIndependent.sum_typeₓ'. -/
 theorem LinearIndependent.sum_type {v' : ι' → M} (hv : LinearIndependent R v)
     (hv' : LinearIndependent R v')
     (h : Disjoint (Submodule.span R (range v)) (Submodule.span R (range v'))) :
@@ -716,12 +1010,24 @@ theorem LinearIndependent.sum_type {v' : ι' → M} (hv : LinearIndependent R v)
   linearIndependent_sum.2 ⟨hv, hv', h⟩
 #align linear_independent.sum_type LinearIndependent.sum_type
 
+/- warning: linear_independent.union -> LinearIndependent.union is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_independent.union LinearIndependent.unionₓ'. -/
 theorem LinearIndependent.union {s t : Set M} (hs : LinearIndependent R (fun x => x : s → M))
     (ht : LinearIndependent R (fun x => x : t → M)) (hst : Disjoint (span R s) (span R t)) :
     LinearIndependent R (fun x => x : s ∪ t → M) :=
   (hs.sum_type ht <| by simpa).to_subtype_range' <| by simp
 #align linear_independent.union LinearIndependent.union
 
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+Case conversion may be inaccurate. Consider using '#align linear_independent_Union_finite_subtype linearIndependent_unionᵢ_finite_subtypeₓ'. -/
 theorem linearIndependent_unionᵢ_finite_subtype {ι : Type _} {f : ι → Set M}
     (hl : ∀ i, LinearIndependent R (fun x => x : f i → M))
     (hd : ∀ i, ∀ t : Set ι, t.Finite → i ∉ t → Disjoint (span R (f i)) (⨆ i ∈ t, span R (f i))) :
@@ -741,7 +1047,13 @@ theorem linearIndependent_unionᵢ_finite_subtype {ι : Type _} {f : ι → Set
     exact hd i s s.finite_to_set his
 #align linear_independent_Union_finite_subtype linearIndependent_unionᵢ_finite_subtype
 
-theorem linearIndependent_Union_finite {η : Type _} {ιs : η → Type _} {f : ∀ j : η, ιs j → M}
+/- warning: linear_independent_Union_finite -> linearIndependent_unionᵢ_finite is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {η : Type.{u3}} {ιs : η -> Type.{u4}} {f : forall (j : η), (ιs j) -> M}, (forall (j : η), LinearIndependent.{u4, u1, u2} (ιs j) R M (f j) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) -> (forall (i : η) (t : Set.{u3} η), (Set.Finite.{u3} η t) -> (Not (Membership.Mem.{u3, u3} η (Set.{u3} η) (Set.hasMem.{u3} η) i t)) -> (Disjoint.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)) (Submodule.orderBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u4} M (ιs i) (f i))) (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) η (fun (i : η) => supᵢ.{u2, 0} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5))) (Membership.Mem.{u3, u3} η (Set.{u3} η) (Set.hasMem.{u3} η) i t) (fun (H : Membership.Mem.{u3, u3} η (Set.{u3} η) (Set.hasMem.{u3} η) i t) => Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u4} M (ιs i) (f i))))))) -> (LinearIndependent.{max u3 u4, u1, u2} (Sigma.{u3, u4} η (fun (j : η) => ιs j)) R M (fun (ji : Sigma.{u3, u4} η (fun (j : η) => ιs j)) => f (Sigma.fst.{u3, u4} η (fun (j : η) => ιs j) ji) (Sigma.snd.{u3, u4} η (fun (j : η) => ιs j) ji)) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {η : Type.{u4}} {ιs : η -> Type.{u3}} {f : forall (j : η), (ιs j) -> M}, (forall (j : η), LinearIndependent.{u3, u2, u1} (ιs j) R M (f j) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (forall (i : η) (t : Set.{u4} η), (Set.Finite.{u4} η t) -> (Not (Membership.mem.{u4, u4} η (Set.{u4} η) (Set.instMembershipSet.{u4} η) i t)) -> (Disjoint.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M (ιs i) (f i))) (supᵢ.{u1, succ u4} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))) η (fun (i : η) => supᵢ.{u1, 0} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))) (Membership.mem.{u4, u4} η (Set.{u4} η) (Set.instMembershipSet.{u4} η) i t) (fun (H : Membership.mem.{u4, u4} η (Set.{u4} η) (Set.instMembershipSet.{u4} η) i t) => Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Set.range.{u1, succ u3} M (ιs i) (f i))))))) -> (LinearIndependent.{max u4 u3, u2, u1} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R M (fun (ji : Sigma.{u4, u3} η (fun (j : η) => ιs j)) => f (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji) (Sigma.snd.{u4, u3} η (fun (j : η) => ιs j) ji)) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5)
+Case conversion may be inaccurate. Consider using '#align linear_independent_Union_finite linearIndependent_unionᵢ_finiteₓ'. -/
+theorem linearIndependent_unionᵢ_finite {η : Type _} {ιs : η → Type _} {f : ∀ j : η, ιs j → M}
     (hindep : ∀ j, LinearIndependent R (f j))
     (hd :
       ∀ i,
@@ -769,7 +1081,7 @@ theorem linearIndependent_Union_finite {η : Type _} {ιs : η → Type _} {f :
       exact False.elim ((hindep x₁).NeZero _ h0)
   rw [range_sigma_eq_Union_range]
   apply linearIndependent_unionᵢ_finite_subtype (fun j => (hindep j).to_subtype_range) hd
-#align linear_independent_Union_finite linearIndependent_Union_finite
+#align linear_independent_Union_finite linearIndependent_unionᵢ_finite
 
 end Subtype
 
@@ -777,6 +1089,12 @@ section repr
 
 variable (hv : LinearIndependent R v)
 
+/- warning: linear_independent.total_equiv -> LinearIndependent.totalEquiv is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearEquiv.{u2, u2, max u1 u2, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearIndependent.totalEquiv._proof_1.{u2} R _inst_1) (LinearIndependent.totalEquiv._proof_2.{u2} R _inst_1) (Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.addCommMonoid.{u1, u2} ι R (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.module.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Submodule.module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))))
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)], (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) -> (LinearEquiv.{u2, u2, max u2 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.instSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5)) x (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v)))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1))))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u2, u2} ι R R (Ring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonUnitalRing.{u2} R _inst_1)))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} R _inst_1)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5 (Set.range.{u3, succ u1} M ι v))))
+Case conversion may be inaccurate. Consider using '#align linear_independent.total_equiv LinearIndependent.totalEquivₓ'. -/
 /-- Canonical isomorphism between linear combinations and the span of linearly independent vectors.
 -/
 @[simps (config := { rhsMd := semireducible })]
@@ -796,6 +1114,12 @@ def LinearIndependent.totalEquiv (hv : LinearIndependent R v) : (ι →₀ R) 
     apply mem_range_self l
 #align linear_independent.total_equiv LinearIndependent.totalEquiv
 
+/- warning: linear_independent.repr -> LinearIndependent.repr is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align linear_independent.repr LinearIndependent.reprₓ'. -/
 /-- Linear combination representing a vector in the span of linearly independent vectors.
 
 Given a family of linearly independent vectors, we can represent any vector in their span as
@@ -805,24 +1129,54 @@ def LinearIndependent.repr (hv : LinearIndependent R v) : span R (range v) →
   hv.totalEquiv.symm
 #align linear_independent.repr LinearIndependent.repr
 
+/- warning: linear_independent.total_repr -> LinearIndependent.total_repr is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_independent.total_repr LinearIndependent.total_reprₓ'. -/
 @[simp]
 theorem LinearIndependent.total_repr (x) : Finsupp.total ι M R v (hv.repr x) = x :=
   Subtype.ext_iff.1 (LinearEquiv.apply_symm_apply hv.totalEquiv x)
 #align linear_independent.total_repr LinearIndependent.total_repr
 
+/- warning: linear_independent.total_comp_repr -> LinearIndependent.total_comp_repr is a dubious translation:
+lean 3 declaration is
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} 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)))) (Finsupp.total.{u3, u2, u1} ι M R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 v) (LinearIndependent.repr.{u3, u1, u2} ι R M v _inst_1 _inst_2 _inst_5 hv)) (Submodule.subtype.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5 (Set.range.{u2, succ u3} M ι v)))
+Case conversion may be inaccurate. Consider using '#align linear_independent.total_comp_repr LinearIndependent.total_comp_reprₓ'. -/
 theorem LinearIndependent.total_comp_repr :
     (Finsupp.total ι M R v).comp hv.repr = Submodule.subtype _ :=
   LinearMap.ext <| hv.total_repr
 #align linear_independent.total_comp_repr LinearIndependent.total_comp_repr
 
+/- warning: linear_independent.repr_ker -> LinearIndependent.repr_ker is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align linear_independent.repr_ker LinearIndependent.repr_kerₓ'. -/
 theorem LinearIndependent.repr_ker : hv.repr.ker = ⊥ := by
   rw [LinearIndependent.repr, LinearEquiv.ker]
 #align linear_independent.repr_ker LinearIndependent.repr_ker
 
+/- warning: linear_independent.repr_range -> LinearIndependent.repr_range is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align linear_independent.repr_range LinearIndependent.repr_rangeₓ'. -/
 theorem LinearIndependent.repr_range : hv.repr.range = ⊤ := by
   rw [LinearIndependent.repr, LinearEquiv.range]
 #align linear_independent.repr_range LinearIndependent.repr_range
 
+/- warning: linear_independent.repr_eq -> LinearIndependent.repr_eq is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (hv : LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) {l : Finsupp.{u1, u2} ι R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))))} {x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5) M (Submodule.setLike.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq LinearIndependent.repr_eqₓ'. -/
 theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M R v l = ↑x) :
     hv.repr x = l :=
   by
@@ -839,12 +1193,24 @@ theorem LinearIndependent.repr_eq {l : ι →₀ R} {x} (eq : Finsupp.total ι M
   rfl
 #align linear_independent.repr_eq LinearIndependent.repr_eq
 
+/- warning: linear_independent.repr_eq_single -> LinearIndependent.repr_eq_single is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align linear_independent.repr_eq_single LinearIndependent.repr_eq_singleₓ'. -/
 theorem LinearIndependent.repr_eq_single (i) (x) (hx : ↑x = v i) : hv.repr x = Finsupp.single i 1 :=
   by
   apply hv.repr_eq
   simp [Finsupp.total_single, hx]
 #align linear_independent.repr_eq_single LinearIndependent.repr_eq_single
 
+/- warning: linear_independent.span_repr_eq -> LinearIndependent.span_repr_eq is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align linear_independent.span_repr_eq LinearIndependent.span_repr_eqₓ'. -/
 theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
     Span.repr R (Set.range v) x = (hv.repr x).equivMapDomain (Equiv.ofInjective _ hv.Injective) :=
   by
@@ -860,6 +1226,12 @@ theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
   simp [← p]
 #align linear_independent.span_repr_eq LinearIndependent.span_repr_eq
 
+/- warning: linear_independent_iff_not_smul_mem_span -> linearIndependent_iff_not_smul_mem_span is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_independent_iff_not_smul_mem_span linearIndependent_iff_not_smul_mem_spanₓ'. -/
 -- TODO: why is this so slow?
 theorem linearIndependent_iff_not_smul_mem_span :
     LinearIndependent R v ↔ ∀ (i : ι) (a : R), a • v i ∈ span R (v '' (univ \ {i})) → a = 0 :=
@@ -883,6 +1255,12 @@ theorem linearIndependent_iff_not_smul_mem_span :
       · simp [hl]⟩
 #align linear_independent_iff_not_smul_mem_span linearIndependent_iff_not_smul_mem_span
 
+/- warning: linear_independent.independent_span_singleton -> LinearIndependent.independent_span_singleton is a dubious translation:
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+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} {v : ι -> M} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (CompleteLattice.Independent.{succ u3, u1} ι (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (fun (i : ι) => Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) (v i))))
+Case conversion may be inaccurate. Consider using '#align linear_independent.independent_span_singleton LinearIndependent.independent_span_singletonₓ'. -/
 /-- See also `complete_lattice.independent_iff_linear_independent_of_ne_zero`. -/
 theorem LinearIndependent.independent_span_singleton (hv : LinearIndependent R v) :
     CompleteLattice.Independent fun i => R ∙ v i :=
@@ -901,6 +1279,12 @@ theorem LinearIndependent.independent_span_singleton (hv : LinearIndependent R v
 
 variable (R)
 
+/- warning: exists_maximal_independent' -> exists_maximal_independent' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align exists_maximal_independent' exists_maximal_independent'ₓ'. -/
 theorem exists_maximal_independent' (s : ι → M) :
     ∃ I : Set ι,
       (LinearIndependent R fun x : I => s x) ∧
@@ -928,6 +1312,12 @@ theorem exists_maximal_independent' (s : ι → M) :
   exact ⟨I, hli, fun J hsub hli => Set.Subset.antisymm hsub (hmax ⟨J, hli⟩ hsub)⟩
 #align exists_maximal_independent' exists_maximal_independent'
 
+/- warning: exists_maximal_independent -> exists_maximal_independent is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align exists_maximal_independent exists_maximal_independentₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (i «expr ∉ » I) -/
 theorem exists_maximal_independent (s : ι → M) :
     ∃ I : Set ι,
@@ -967,6 +1357,12 @@ theorem exists_maximal_independent (s : ι → M) :
 
 end repr
 
+/- warning: surjective_of_linear_independent_of_span -> surjective_of_linearIndependent_of_span is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align surjective_of_linear_independent_of_span surjective_of_linearIndependent_of_spanₓ'. -/
 theorem surjective_of_linearIndependent_of_span [Nontrivial R] (hv : LinearIndependent R v)
     (f : ι' ↪ ι) (hss : range v ⊆ span R (range (v ∘ f))) : Surjective f :=
   by
@@ -990,6 +1386,12 @@ theorem surjective_of_linearIndependent_of_span [Nontrivial R] (hv : LinearIndep
   exact hi'.2
 #align surjective_of_linear_independent_of_span surjective_of_linearIndependent_of_span
 
+/- warning: eq_of_linear_independent_of_span_subtype -> eq_of_linearIndependent_of_span_subtype is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align eq_of_linear_independent_of_span_subtype eq_of_linearIndependent_of_span_subtypeₓ'. -/
 theorem eq_of_linearIndependent_of_span_subtype [Nontrivial R] {s t : Set M}
     (hs : LinearIndependent R (fun x => x : s → M)) (h : t ⊆ s) (hst : s ⊆ span R t) : s = t :=
   by
@@ -1010,6 +1412,12 @@ theorem eq_of_linearIndependent_of_span_subtype [Nontrivial R] {s t : Set M}
 
 open LinearMap
 
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+Case conversion may be inaccurate. Consider using '#align linear_independent.image_subtype LinearIndependent.image_subtypeₓ'. -/
 theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
     (hs : LinearIndependent R (fun x => x : s → M)) (hf_inj : Disjoint (span R s) f.ker) :
     LinearIndependent R (fun x => x : f '' s → M') :=
@@ -1019,6 +1427,12 @@ theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
   simp [Set.range_comp f]
 #align linear_independent.image_subtype LinearIndependent.image_subtype
 
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+Case conversion may be inaccurate. Consider using '#align linear_independent.inl_union_inr LinearIndependent.inl_union_inrₓ'. -/
 theorem LinearIndependent.inl_union_inr {s : Set M} {t : Set M'}
     (hs : LinearIndependent R (fun x => x : s → M))
     (ht : LinearIndependent R (fun x => x : t → M')) :
@@ -1029,6 +1443,12 @@ theorem LinearIndependent.inl_union_inr {s : Set M} {t : Set M'}
   simp [disjoint_iff, prod_inf_prod]
 #align linear_independent.inl_union_inr LinearIndependent.inl_union_inr
 
+/- warning: linear_independent_inl_union_inr' -> linearIndependent_inl_union_inr' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_independent_inl_union_inr' linearIndependent_inl_union_inr'ₓ'. -/
 theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv : LinearIndependent R v)
     (hv' : LinearIndependent R v') :
     LinearIndependent R (Sum.elim (inl R M M' ∘ v) (inr R M M' ∘ v')) :=
@@ -1037,6 +1457,12 @@ theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv :
       simp only [span_le, range_coe, range_comp_subset_range]
 #align linear_independent_inl_union_inr' linearIndependent_inl_union_inr'
 
+/- warning: linear_independent_monoid_hom -> linearIndependent_monoidHom is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_independent_monoid_hom linearIndependent_monoidHomₓ'. -/
 -- See, for example, Keith Conrad's note
 --  <https://kconrad.math.uconn.edu/blurbs/galoistheory/linearchar.pdf>
 /-- Dedekind's linear independence of characters -/
@@ -1134,6 +1560,12 @@ theorem linearIndependent_monoidHom (G : Type _) [Monoid G] (L : Type _) [CommRi
             ⟨h4, h3⟩
 #align linear_independent_monoid_hom linearIndependent_monoidHom
 
+/- warning: le_of_span_le_span -> le_of_span_le_span is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Nontrivial.{u2} R] {s : Set.{u1} M} {t : Set.{u1} M} {u : Set.{u1} M}, (LinearIndependent.{u1, u2, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x u)) R M (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x u)) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) -> (HasSubset.Subset.{u1} (Set.{u1} M) (Set.instHasSubsetSet.{u1} M) s u) -> (HasSubset.Subset.{u1} (Set.{u1} M) (Set.instHasSubsetSet.{u1} M) t u) -> (LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5))))) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 s) (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_5 t)) -> (HasSubset.Subset.{u1} (Set.{u1} M) (Set.instHasSubsetSet.{u1} M) s t)
+Case conversion may be inaccurate. Consider using '#align le_of_span_le_span le_of_span_le_spanₓ'. -/
 theorem le_of_span_le_span [Nontrivial R] {s t u : Set M} (hl : LinearIndependent R (coe : u → M))
     (hsu : s ⊆ u) (htu : t ⊆ u) (hst : span R s ≤ span R t) : s ⊆ t :=
   by
@@ -1143,6 +1575,12 @@ theorem le_of_span_le_span [Nontrivial R] {s t u : Set M} (hl : LinearIndependen
   rw [← this]; apply Set.subset_union_left
 #align le_of_span_le_span le_of_span_le_span
 
+/- warning: span_le_span_iff -> span_le_span_iff is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align span_le_span_iff span_le_span_iffₓ'. -/
 theorem span_le_span_iff [Nontrivial R] {s t u : Set M} (hl : LinearIndependent R (coe : u → M))
     (hsu : s ⊆ u) (htu : t ⊆ u) : span R s ≤ span R t ↔ s ⊆ t :=
   ⟨le_of_span_le_span hl hsu htu, span_mono⟩
@@ -1158,6 +1596,12 @@ variable [Module R M] [NoZeroSMulDivisors R M] [Module R M']
 
 variable {v : ι → M} {s t : Set M} {x y z : M}
 
+/- warning: linear_independent_unique_iff -> linearIndependent_unique_iff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : Nontrivial.{u2} R] [_inst_3 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] [_inst_6 : NoZeroSMulDivisors.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5))))] (v : ι -> M) [_inst_8 : Unique.{succ u1} ι], Iff (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Ne.{succ u3} M (v (Inhabited.default.{succ u1} ι (Unique.inhabited.{succ u1} ι _inst_8))) (OfNat.ofNat.{u3} M 0 (OfNat.mk.{u3} M 0 (Zero.zero.{u3} M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_3)))))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align linear_independent_unique_iff linearIndependent_unique_iffₓ'. -/
 theorem linearIndependent_unique_iff (v : ι → M) [Unique ι] :
     LinearIndependent R v ↔ v default ≠ 0 :=
   by
@@ -1167,9 +1611,21 @@ theorem linearIndependent_unique_iff (v : ι → M) [Unique ι] :
   exact one_ne_zero (Finsupp.single_eq_zero.1 this)
 #align linear_independent_unique_iff linearIndependent_unique_iff
 
+/- warning: linear_independent_unique -> linearIndependent_unique is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Ring.{u2} R] [_inst_2 : Nontrivial.{u2} R] [_inst_3 : AddCommGroup.{u3} M] [_inst_5 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] [_inst_6 : NoZeroSMulDivisors.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)))) (Module.toMulActionWithZero.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5))))] (v : ι -> M) [_inst_8 : Unique.{succ u1} ι], (Ne.{succ u3} M (v (Inhabited.default.{succ u1} ι (Unique.inhabited.{succ u1} ι _inst_8))) (OfNat.ofNat.{u3} M 0 (OfNat.mk.{u3} M 0 (Zero.zero.{u3} M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (SubNegMonoid.toAddMonoid.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_3))))))))) -> (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5)
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : Nontrivial.{u2} R] [_inst_3 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3)] [_inst_6 : NoZeroSMulDivisors.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_3))))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_3))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_5))))] (v : ι -> M) [_inst_8 : Unique.{succ u3} ι], (Ne.{succ u1} M (v (Inhabited.default.{succ u3} ι (Unique.instInhabited.{succ u3} ι _inst_8))) (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_3)))))))) -> (LinearIndependent.{u3, u2, u1} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_5)
+Case conversion may be inaccurate. Consider using '#align linear_independent_unique linearIndependent_uniqueₓ'. -/
 alias linearIndependent_unique_iff ↔ _ linearIndependent_unique
 #align linear_independent_unique linearIndependent_unique
 
+/- warning: linear_independent_singleton -> linearIndependent_singleton is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align linear_independent_singleton linearIndependent_singletonₓ'. -/
 theorem linearIndependent_singleton {x : M} (hx : x ≠ 0) :
     LinearIndependent R (fun x => x : ({x} : Set M) → M) :=
   linearIndependent_unique coe hx
@@ -1194,6 +1650,12 @@ variable {v : ι → V} {s t : Set V} {x y z : V}
 
 open Submodule
 
+/- warning: mem_span_insert_exchange -> mem_span_insert_exchange is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mem_span_insert_exchange mem_span_insert_exchangeₓ'. -/
 /- TODO: some of the following proofs can generalized with a zero_ne_one predicate type class
    (instead of a data containing type class) -/
 theorem mem_span_insert_exchange :
@@ -1208,6 +1670,12 @@ theorem mem_span_insert_exchange :
   simp [a0, smul_add, smul_smul]
 #align mem_span_insert_exchange mem_span_insert_exchange
 
+/- warning: linear_independent_iff_not_mem_span -> linearIndependent_iff_not_mem_span is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align linear_independent_iff_not_mem_span linearIndependent_iff_not_mem_spanₓ'. -/
 theorem linearIndependent_iff_not_mem_span :
     LinearIndependent K v ↔ ∀ i, v i ∉ span K (v '' (univ \ {i})) :=
   by
@@ -1220,6 +1688,12 @@ theorem linearIndependent_iff_not_mem_span :
     exact False.elim (h _ ((smul_mem_iff _ ha').1 ha))
 #align linear_independent_iff_not_mem_span linearIndependent_iff_not_mem_span
 
+/- warning: linear_independent.insert -> LinearIndependent.insert is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_independent.insert LinearIndependent.insertₓ'. -/
 theorem LinearIndependent.insert (hs : LinearIndependent K (fun b => b : s → V))
     (hx : x ∉ span K s) : LinearIndependent K (fun b => b : insert x s → V) :=
   by
@@ -1229,6 +1703,12 @@ theorem LinearIndependent.insert (hs : LinearIndependent K (fun b => b : s → V
   rwa [disjoint_span_singleton' x0]
 #align linear_independent.insert LinearIndependent.insert
 
+/- warning: linear_independent_option' -> linearIndependent_option' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_independent_option' linearIndependent_option'ₓ'. -/
 theorem linearIndependent_option' :
     LinearIndependent K (fun o => Option.casesOn' o x v : Option ι → V) ↔
       LinearIndependent K v ∧ x ∉ Submodule.span K (range v) :=
@@ -1241,18 +1721,36 @@ theorem linearIndependent_option' :
   exact h.2 (zero_mem _)
 #align linear_independent_option' linearIndependent_option'
 
+/- warning: linear_independent.option -> LinearIndependent.option is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_independent.option LinearIndependent.optionₓ'. -/
 theorem LinearIndependent.option (hv : LinearIndependent K v)
     (hx : x ∉ Submodule.span K (range v)) :
     LinearIndependent K (fun o => Option.casesOn' o x v : Option ι → V) :=
   linearIndependent_option'.2 ⟨hv, hx⟩
 #align linear_independent.option LinearIndependent.option
 
+/- warning: linear_independent_option -> linearIndependent_option is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align linear_independent_option linearIndependent_optionₓ'. -/
 theorem linearIndependent_option {v : Option ι → V} :
     LinearIndependent K v ↔
       LinearIndependent K (v ∘ coe : ι → V) ∧ v none ∉ Submodule.span K (range (v ∘ coe : ι → V)) :=
   by simp only [← linearIndependent_option', Option.casesOn'_none_coe]
 #align linear_independent_option linearIndependent_option
 
+/- warning: linear_independent_insert' -> linearIndependent_insert' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_independent_insert' linearIndependent_insert'ₓ'. -/
 theorem linearIndependent_insert' {ι} {s : Set ι} {a : ι} {f : ι → V} (has : a ∉ s) :
     (LinearIndependent K fun x : insert a s => f x) ↔
       (LinearIndependent K fun x : s => f x) ∧ f a ∉ Submodule.span K (f '' s) :=
@@ -1262,18 +1760,36 @@ theorem linearIndependent_insert' {ι} {s : Set ι} {a : ι} {f : ι → V} (has
   simp [(· ∘ ·), range_comp f]
 #align linear_independent_insert' linearIndependent_insert'
 
+/- warning: linear_independent_insert -> linearIndependent_insert is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_independent_insert linearIndependent_insertₓ'. -/
 theorem linearIndependent_insert (hxs : x ∉ s) :
     (LinearIndependent K fun b : insert x s => (b : V)) ↔
       (LinearIndependent K fun b : s => (b : V)) ∧ x ∉ Submodule.span K s :=
   (@linearIndependent_insert' _ _ _ _ _ _ _ _ id hxs).trans <| by simp
 #align linear_independent_insert linearIndependent_insert
 
+/- warning: linear_independent_pair -> linearIndependent_pair is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_independent_pair linearIndependent_pairₓ'. -/
 theorem linearIndependent_pair {x y : V} (hx : x ≠ 0) (hy : ∀ a : K, a • x ≠ y) :
     LinearIndependent K (coe : ({x, y} : Set V) → V) :=
   pair_comm y x ▸ (linearIndependent_singleton hx).insert <|
     mt mem_span_singleton.1 (not_exists.2 hy)
 #align linear_independent_pair linearIndependent_pair
 
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+Case conversion may be inaccurate. Consider using '#align linear_independent_fin_cons linearIndependent_fin_consₓ'. -/
 theorem linearIndependent_fin_cons {n} {v : Fin n → V} :
     LinearIndependent K (Fin.cons x v : Fin (n + 1) → V) ↔
       LinearIndependent K v ∧ x ∉ Submodule.span K (range v) :=
@@ -1287,12 +1803,24 @@ theorem linearIndependent_fin_cons {n} {v : Fin n → V} :
     rw [comp_app, comp_app, finSuccEquiv_symm_some, Fin.cons_succ]
 #align linear_independent_fin_cons linearIndependent_fin_cons
 
+/- warning: linear_independent_fin_snoc -> linearIndependent_fin_snoc is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_independent_fin_snoc linearIndependent_fin_snocₓ'. -/
 theorem linearIndependent_fin_snoc {n} {v : Fin n → V} :
     LinearIndependent K (Fin.snoc v x : Fin (n + 1) → V) ↔
       LinearIndependent K v ∧ x ∉ Submodule.span K (range v) :=
   by rw [Fin.snoc_eq_cons_rotate, linearIndependent_equiv, linearIndependent_fin_cons]
 #align linear_independent_fin_snoc linearIndependent_fin_snoc
 
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+Case conversion may be inaccurate. Consider using '#align linear_independent.fin_cons LinearIndependent.fin_consₓ'. -/
 /-- See `linear_independent.fin_cons'` for an uglier version that works if you
 only have a module over a semiring. -/
 theorem LinearIndependent.fin_cons {n} {v : Fin n → V} (hv : LinearIndependent K v)
@@ -1300,24 +1828,48 @@ theorem LinearIndependent.fin_cons {n} {v : Fin n → V} (hv : LinearIndependent
   linearIndependent_fin_cons.2 ⟨hv, hx⟩
 #align linear_independent.fin_cons LinearIndependent.fin_cons
 
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+Case conversion may be inaccurate. Consider using '#align linear_independent_fin_succ linearIndependent_fin_succₓ'. -/
 theorem linearIndependent_fin_succ {n} {v : Fin (n + 1) → V} :
     LinearIndependent K v ↔
       LinearIndependent K (Fin.tail v) ∧ v 0 ∉ Submodule.span K (range <| Fin.tail v) :=
   by rw [← linearIndependent_fin_cons, Fin.cons_self_tail]
 #align linear_independent_fin_succ linearIndependent_fin_succ
 
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+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align linear_independent_fin_succ' linearIndependent_fin_succ'ₓ'. -/
 theorem linearIndependent_fin_succ' {n} {v : Fin (n + 1) → V} :
     LinearIndependent K v ↔
       LinearIndependent K (Fin.init v) ∧ v (Fin.last _) ∉ Submodule.span K (range <| Fin.init v) :=
   by rw [← linearIndependent_fin_snoc, Fin.snoc_init_self]
 #align linear_independent_fin_succ' linearIndependent_fin_succ'
 
+/- warning: linear_independent_fin2 -> linearIndependent_fin2 is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align linear_independent_fin2 linearIndependent_fin2ₓ'. -/
 theorem linearIndependent_fin2 {f : Fin 2 → V} :
     LinearIndependent K f ↔ f 1 ≠ 0 ∧ ∀ a : K, a • f 1 ≠ f 0 := by
   rw [linearIndependent_fin_succ, linearIndependent_unique_iff, range_unique, mem_span_singleton,
     not_exists, show Fin.tail f default = f 1 by rw [← Fin.succ_zero_eq_one] <;> rfl]
 #align linear_independent_fin2 linearIndependent_fin2
 
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+Case conversion may be inaccurate. Consider using '#align exists_linear_independent_extension exists_linearIndependent_extensionₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (b «expr ⊆ » t) -/
 theorem exists_linearIndependent_extension (hs : LinearIndependent K (coe : s → V)) (hst : s ⊆ t) :
     ∃ (b : _)(_ : b ⊆ t), s ⊆ b ∧ t ⊆ span K b ∧ LinearIndependent K (coe : b → V) :=
@@ -1337,6 +1889,12 @@ theorem exists_linearIndependent_extension (hs : LinearIndependent K (coe : s 
 
 variable (K t)
 
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+Case conversion may be inaccurate. Consider using '#align exists_linear_independent exists_linearIndependentₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (b «expr ⊆ » t) -/
 theorem exists_linearIndependent :
     ∃ (b : _)(_ : b ⊆ t), span K b = span K t ∧ LinearIndependent K (coe : b → V) :=
@@ -1348,31 +1906,57 @@ theorem exists_linearIndependent :
 
 variable {K t}
 
+#print LinearIndependent.extend /-
 /-- `linear_independent.extend` adds vectors to a linear independent set `s ⊆ t` until it spans
 all elements of `t`. -/
 noncomputable def LinearIndependent.extend (hs : LinearIndependent K (fun x => x : s → V))
     (hst : s ⊆ t) : Set V :=
   Classical.choose (exists_linearIndependent_extension hs hst)
 #align linear_independent.extend LinearIndependent.extend
+-/
 
+/- warning: linear_independent.extend_subset -> LinearIndependent.extend_subset is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_independent.extend_subset LinearIndependent.extend_subsetₓ'. -/
 theorem LinearIndependent.extend_subset (hs : LinearIndependent K (fun x => x : s → V))
     (hst : s ⊆ t) : hs.extend hst ⊆ t :=
   let ⟨hbt, hsb, htb, hli⟩ := Classical.choose_spec (exists_linearIndependent_extension hs hst)
   hbt
 #align linear_independent.extend_subset LinearIndependent.extend_subset
 
+/- warning: linear_independent.subset_extend -> LinearIndependent.subset_extend is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_independent.subset_extend LinearIndependent.subset_extendₓ'. -/
 theorem LinearIndependent.subset_extend (hs : LinearIndependent K (fun x => x : s → V))
     (hst : s ⊆ t) : s ⊆ hs.extend hst :=
   let ⟨hbt, hsb, htb, hli⟩ := Classical.choose_spec (exists_linearIndependent_extension hs hst)
   hsb
 #align linear_independent.subset_extend LinearIndependent.subset_extend
 
+/- warning: linear_independent.subset_span_extend -> LinearIndependent.subset_span_extend is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_independent.subset_span_extend LinearIndependent.subset_span_extendₓ'. -/
 theorem LinearIndependent.subset_span_extend (hs : LinearIndependent K (fun x => x : s → V))
     (hst : s ⊆ t) : t ⊆ span K (hs.extend hst) :=
   let ⟨hbt, hsb, htb, hli⟩ := Classical.choose_spec (exists_linearIndependent_extension hs hst)
   htb
 #align linear_independent.subset_span_extend LinearIndependent.subset_span_extend
 
+/- warning: linear_independent.linear_independent_extend -> LinearIndependent.linearIndependent_extend is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_independent.linear_independent_extend LinearIndependent.linearIndependent_extendₓ'. -/
 theorem LinearIndependent.linearIndependent_extend (hs : LinearIndependent K (fun x => x : s → V))
     (hst : s ⊆ t) : LinearIndependent K (coe : hs.extend hst → V) :=
   let ⟨hbt, hsb, htb, hli⟩ := Classical.choose_spec (exists_linearIndependent_extension hs hst)
@@ -1381,6 +1965,12 @@ theorem LinearIndependent.linearIndependent_extend (hs : LinearIndependent K (fu
 
 variable {K V}
 
+/- warning: exists_of_linear_independent_of_finite_span -> exists_of_linearIndependent_of_finite_span is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {s : Set.{u2} V} {t : Finset.{u2} V}, (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} V s) K V (fun (x : Set.Elem.{u2} V s) => Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s) x) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) -> (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) s (SetLike.coe.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 (Finset.toSet.{u2} V t)))) -> (Exists.{succ u2} (Finset.{u2} V) (fun (t' : Finset.{u2} V) => And (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) (Finset.toSet.{u2} V t') (Union.union.{u2} (Set.{u2} V) (Set.instUnionSet.{u2} V) s (Finset.toSet.{u2} V t))) (And (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) s (Finset.toSet.{u2} V t')) (Eq.{1} Nat (Finset.card.{u2} V t') (Finset.card.{u2} V t)))))
+Case conversion may be inaccurate. Consider using '#align exists_of_linear_independent_of_finite_span exists_of_linearIndependent_of_finite_spanₓ'. -/
 -- TODO(Mario): rewrite?
 theorem exists_of_linearIndependent_of_finite_span {t : Finset V}
     (hs : LinearIndependent K (fun x => x : s → V)) (hst : s ⊆ (span K ↑t : Submodule K V)) :
@@ -1444,6 +2034,12 @@ theorem exists_of_linearIndependent_of_finite_span {t : Finset V}
       h.2.1, by simp only [h.2.2, Eq]⟩
 #align exists_of_linear_independent_of_finite_span exists_of_linearIndependent_of_finite_span
 
+/- warning: exists_finite_card_le_of_finite_of_linear_independent_of_span -> exists_finite_card_le_of_finite_of_linearIndependent_of_span is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : DivisionRing.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_4 : Module.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {s : Set.{u1} V} {t : Set.{u1} V} (ht : Set.Finite.{u1} V t), (LinearIndependent.{u1, u2, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) K V (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} V) Type.{u1} (Set.hasCoeToSort.{u1} V) s) V (coeSubtype.{succ u1} V (fun (x : V) => Membership.Mem.{u1, u1} V (Set.{u1} V) (Set.hasMem.{u1} V) x s))))) x) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) -> (HasSubset.Subset.{u1} (Set.{u1} V) (Set.hasSubset.{u1} V) s ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Set.{u1} V) (HasLiftT.mk.{succ u1, succ u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Set.{u1} V) (CoeTCₓ.coe.{succ u1, succ u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) (Set.{u1} V) (SetLike.Set.hasCoeT.{u1, u1} (Submodule.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4) V (Submodule.setLike.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4)))) (Submodule.span.{u2, u1} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_4 t))) -> (Exists.{0} (Set.Finite.{u1} V s) (fun (h : Set.Finite.{u1} V s) => LE.le.{0} Nat Nat.hasLe (Finset.card.{u1} V (Set.Finite.toFinset.{u1} V s h)) (Finset.card.{u1} V (Set.Finite.toFinset.{u1} V t ht))))
+but is expected to have type
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {s : Set.{u2} V} {t : Set.{u2} V} (ht : Set.Finite.{u2} V t), (LinearIndependent.{u2, u1, u2} (Set.Elem.{u2} V s) K V (fun (x : Set.Elem.{u2} V s) => Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s) x) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) -> (HasSubset.Subset.{u2} (Set.{u2} V) (Set.instHasSubsetSet.{u2} V) s (SetLike.coe.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4) (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_4 t))) -> (Exists.{0} (Set.Finite.{u2} V s) (fun (h : Set.Finite.{u2} V s) => LE.le.{0} Nat instLENat (Finset.card.{u2} V (Set.Finite.toFinset.{u2} V s h)) (Finset.card.{u2} V (Set.Finite.toFinset.{u2} V t ht))))
+Case conversion may be inaccurate. Consider using '#align exists_finite_card_le_of_finite_of_linear_independent_of_span exists_finite_card_le_of_finite_of_linearIndependent_of_spanₓ'. -/
 theorem exists_finite_card_le_of_finite_of_linearIndependent_of_span (ht : t.Finite)
     (hs : LinearIndependent K (fun x => x : s → V)) (hst : s ⊆ span K t) :
     ∃ h : s.Finite, h.toFinset.card ≤ ht.toFinset.card :=

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore: adapt to multiple goal linter 1 (#12338)

A PR accompanying #12339.

Zulip discussion

45f93f3f

Diff

@@ -835,8 +835,8 @@ theorem linearIndependent_iUnion_finite {η : Type*} {ιs : η → Type*} {f : 
   apply LinearIndependent.of_subtype_range
   · rintro ⟨x₁, x₂⟩ ⟨y₁, y₂⟩ hxy
     by_cases h_cases : x₁ = y₁
-    subst h_cases
-    · apply Sigma.eq
+    · subst h_cases
+      apply Sigma.eq
       rw [LinearIndependent.injective (hindep _) hxy]
       rfl
     · have h0 : f x₁ x₂ = 0 := by
@@ -866,7 +866,7 @@ def LinearIndependent.totalEquiv (hv : LinearIndependent R v) :
   apply LinearEquiv.ofBijective (LinearMap.codRestrict (span R (range v)) (Finsupp.total ι M R v) _)
   constructor
   · rw [← LinearMap.ker_eq_bot, LinearMap.ker_codRestrict]
-    apply hv
+    · apply hv
     · intro l
       rw [← Finsupp.range_total]
       rw [LinearMap.mem_range]

fix: generalize index types of iSup to Sort (#12114)

This breaks a few simp proofs which were expecting these lemmas to apply to the data binders but not the prop binders.

16e2255a

Diff

@@ -973,12 +973,14 @@ theorem LinearIndependent.independent_span_singleton (hv : LinearIndependent R v
   refine' CompleteLattice.independent_def.mp fun i => _
   rw [disjoint_iff_inf_le]
   intro m hm
-  simp only [mem_inf, mem_span_singleton, iSup_subtype', ← span_range_eq_iSup] at hm
+  simp only [mem_inf, mem_span_singleton, iSup_subtype'] at hm
+  rw [← span_range_eq_iSup] at hm
   obtain ⟨⟨r, rfl⟩, hm⟩ := hm
   suffices r = 0 by simp [this]
   apply linearIndependent_iff_not_smul_mem_span.mp hv i
   -- Porting note: The original proof was using `convert hm`.
-  suffices v '' (univ \ {i}) = range fun j : { j // j ≠ i } => v j by rwa [this]
+  suffices v '' (univ \ {i}) = range fun j : { j // j ≠ i } => v j by
+    rwa [this]
   ext
   simp
 #align linear_independent.independent_span_singleton LinearIndependent.independent_span_singleton

chore: split Subsingleton,Nontrivial off of Data.Set.Basic (#11832)

Moves definition of and lemmas related to Set.Subsingleton and Set.Nontrivial to a new file, so that Basic can be shorter.

493a947e

Diff

@@ -10,7 +10,7 @@ import Mathlib.SetTheory.Cardinal.Basic
 import Mathlib.Tactic.FinCases
 import Mathlib.Tactic.LinearCombination
 import Mathlib.Lean.Expr.ExtraRecognizers
-import Mathlib.Data.Set.Basic
+import Mathlib.Data.Set.Subsingleton
 
 #align_import linear_algebra.linear_independent from "leanprover-community/mathlib"@"9d684a893c52e1d6692a504a118bfccbae04feeb"

chore: remove porting notes about redundant binder updates (#12101)

All these are about some code (now commented out) which performs a (now) redundant binder information update. I don't see how this is useful information going forward, hence propose simply deleting them.

33c3101f

Diff

@@ -1460,8 +1460,6 @@ theorem LinearIndependent.linearIndependent_extend (hs : LinearIndependent K (fu
   hli
 #align linear_independent.linear_independent_extend LinearIndependent.linearIndependent_extend
 
--- variable {K V} -- Porting note: Redundant binder annotation update.
-
 -- TODO(Mario): rewrite?
 theorem exists_of_linearIndependent_of_finite_span {t : Finset V}
     (hs : LinearIndependent K (fun x => x : s → V)) (hst : s ⊆ (span K ↑t : Submodule K V)) :

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

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

75c86f04

Diff

@@ -91,7 +91,6 @@ variable {M : Type*} {M' M'' : Type*} {V : Type u} {V' : Type*}
 section Module
 
 variable {v : ι → M}
-
 variable [Semiring R] [AddCommMonoid M] [AddCommMonoid M'] [AddCommMonoid M'']
 variable [Module R M] [Module R M'] [Module R M'']
 variable {a b : R} {x y : M}
@@ -1241,9 +1240,7 @@ end Module
 section Nontrivial
 
 variable [Ring R] [Nontrivial R] [AddCommGroup M] [AddCommGroup M']
-
 variable [Module R M] [NoZeroSMulDivisors R M] [Module R M']
-
 variable {v : ι → M} {s t : Set M} {x y z : M}
 
 theorem linearIndependent_unique_iff (v : ι → M) [Unique ι] :
@@ -1274,9 +1271,7 @@ These can be considered generalizations of properties of linear independence in
 section Module
 
 variable [DivisionRing K] [AddCommGroup V] [AddCommGroup V']
-
 variable [Module K V] [Module K V']
-
 variable {v : ι → V} {s t : Set V} {x y z : V}
 
 open Submodule

chore: remove useless tactics (#11333)

The removal of some pointless tactics flagged by #11308.

ee18bf38

Diff

@@ -518,8 +518,7 @@ theorem linearIndependent_iUnion_of_directed {η : Type*} {s : η → Set M} (hs
     (h : ∀ i, LinearIndependent R (fun x => x : s i → M)) :
     LinearIndependent R (fun x => x : (⋃ i, s i) → M) := by
   by_cases hη : Nonempty η
-  · skip
-    refine' linearIndependent_of_finite (⋃ i, s i) fun t ht ft => _
+  · refine' linearIndependent_of_finite (⋃ i, s i) fun t ht ft => _
     rcases finite_subset_iUnion ft ht with ⟨I, fi, hI⟩
     rcases hs.finset_le fi.toFinset with ⟨i, hi⟩
     exact (h i).mono (Subset.trans hI <| iUnion₂_subset fun j hj => hi j (fi.mem_toFinset.2 hj))

chore: move Mathlib to v4.7.0-rc1 (#11162)

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

fa48894a

Diff

@@ -570,7 +570,7 @@ theorem LinearIndependent.injective [Nontrivial R] (hv : LinearIndependent R v)
   intro i j hij
   let l : ι →₀ R := Finsupp.single i (1 : R) - Finsupp.single j 1
   have h_total : Finsupp.total ι M R v l = 0 := by
-    simp_rw [LinearMap.map_sub, Finsupp.total_apply]
+    simp_rw [l, LinearMap.map_sub, Finsupp.total_apply]
     simp [hij]
   have h_single_eq : Finsupp.single i (1 : R) = Finsupp.single j 1 := by
     rw [linearIndependent_iff] at hv
@@ -710,7 +710,7 @@ theorem LinearIndependent.eq_of_smul_apply_eq_smul_apply {M : Type*} [AddCommGro
     (h : c • v i = d • v j) : i = j := by
   let l : ι →₀ R := Finsupp.single i c - Finsupp.single j d
   have h_total : Finsupp.total ι M R v l = 0 := by
-    simp_rw [LinearMap.map_sub, Finsupp.total_apply]
+    simp_rw [l, LinearMap.map_sub, Finsupp.total_apply]
     simp [h]
   have h_single_eq : Finsupp.single i c = Finsupp.single j d := by
     rw [linearIndependent_iff] at li

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

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

38bce757

Diff

@@ -409,7 +409,7 @@ theorem linearIndependent_finset_map_embedding_subtype (s : Set M)
   rw [Finset.mem_map] at hx hy
   obtain ⟨a, _ha, rfl⟩ := hx
   obtain ⟨b, _hb, rfl⟩ := hy
-  simp only [imp_self, Subtype.mk_eq_mk]
+  simp only [f, imp_self, Subtype.mk_eq_mk]
 #align linear_independent_finset_map_embedding_subtype linearIndependent_finset_map_embedding_subtype
 
 /-- If every finite set of linearly independent vectors has cardinality at most `n`,
@@ -996,7 +996,7 @@ theorem exists_maximal_independent' (s : ι → M) :
   let r : X → X → Prop := fun I J => I.1 ⊆ J.1
   have key : ∀ c : Set X, IsChain r c → indep (⋃ (I : X) (_ : I ∈ c), I) := by
     intro c hc
-    dsimp
+    dsimp [indep]
     rw [linearIndependent_comp_subtype]
     intro f hsupport hsum
     rcases eq_empty_or_nonempty c with (rfl | hn)
@@ -1023,7 +1023,7 @@ theorem exists_maximal_independent (s : ι → M) :
     specialize hImaximal (I ∪ {i}) (by simp)
     set J := I ∪ {i} with hJ
     have memJ : ∀ {x}, x ∈ J ↔ x = i ∨ x ∈ I := by simp [hJ]
-    have hiJ : i ∈ J := by simp
+    have hiJ : i ∈ J := by simp [J]
     have h := by
       refine mt hImaximal ?_
       · intro h2
@@ -1055,14 +1055,14 @@ theorem surjective_of_linearIndependent_of_span [Nontrivial R] (hv : LinearIndep
   let repr : (span R (range (v ∘ f)) : Type _) → ι' →₀ R := (hv.comp f f.injective).repr
   let l := (repr ⟨v i, hss (mem_range_self i)⟩).mapDomain f
   have h_total_l : Finsupp.total ι M R v l = v i := by
-    dsimp only []
+    dsimp only [l]
     rw [Finsupp.total_mapDomain]
     rw [(hv.comp f f.injective).total_repr]
     -- Porting note: `rfl` isn't necessary.
   have h_total_eq : (Finsupp.total ι M R v) l = (Finsupp.total ι M R v) (Finsupp.single i 1) := by
     rw [h_total_l, Finsupp.total_single, one_smul]
   have l_eq : l = _ := LinearMap.ker_eq_bot.1 hv h_total_eq
-  dsimp only [] at l_eq
+  dsimp only [l] at l_eq
   rw [← Finsupp.embDomain_eq_mapDomain] at l_eq
   rcases Finsupp.single_of_embDomain_single (repr ⟨v i, _⟩) f i (1 : R) zero_ne_one.symm l_eq with
     ⟨i', hi'⟩
@@ -1076,7 +1076,7 @@ theorem eq_of_linearIndependent_of_span_subtype [Nontrivial R] {s t : Set M}
     ⟨fun x => ⟨x.1, h x.2⟩, fun a b hab => Subtype.coe_injective (Subtype.mk.inj hab)⟩
   have h_surj : Surjective f := by
     apply surjective_of_linearIndependent_of_span hs f _
-    convert hst <;> simp [comp]
+    convert hst <;> simp [f, comp]
   show s = t
   · apply Subset.antisymm _ h
     intro x hx

chore: clean up uses of Pi.smul_apply (#9970)

After #9949, Pi.smul_apply can be used in simp again. This PR cleans up some workarounds.

105a8c51

Diff

@@ -613,7 +613,8 @@ theorem LinearIndependent.group_smul {G : Type*} [hG : Group G] [DistribMulActio
     exact (hgs i hi).symm ▸ smul_zero _
   · rw [← hsum, Finset.sum_congr rfl _]
     intros
-    erw [Pi.smul_apply, smul_assoc, smul_comm]
+    dsimp
+    rw [smul_assoc, smul_comm]
 #align linear_independent.group_smul LinearIndependent.group_smul
 
 -- This lemma cannot be proved with `LinearIndependent.group_smul` since the action of

refactor(Data/FunLike): use unbundled inheritance from FunLike (#8386)

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

`simp` not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

c6a73d4f

Diff

@@ -1100,7 +1100,8 @@ theorem LinearIndependent.inl_union_inr {s : Set M} {t : Set M'}
     (ht : LinearIndependent R (fun x => x : t → M')) :
     LinearIndependent R (fun x => x : ↥(inl R M M' '' s ∪ inr R M M' '' t) → M × M') := by
   refine' (hs.image_subtype _).union (ht.image_subtype _) _ <;> [simp; simp; skip]
-  simp only [span_image]
+  -- Note: #8386 had to change `span_image` into `span_image _`
+  simp only [span_image _]
   simp [disjoint_iff, prod_inf_prod]
 #align linear_independent.inl_union_inr LinearIndependent.inl_union_inr

chore(*): shake imports (#10199)

Remove Data.Set.Basic from scripts/noshake.json.
Remove an exception that was used by examples only, move these examples to a new test file.
Drop an exception for Order.Filter.Basic dependency on Control.Traversable.Instances, as the relevant parts were moved to Order.Filter.ListTraverse.
Run lake exe shake --fix.

c167d468

Diff

@@ -10,6 +10,7 @@ import Mathlib.SetTheory.Cardinal.Basic
 import Mathlib.Tactic.FinCases
 import Mathlib.Tactic.LinearCombination
 import Mathlib.Lean.Expr.ExtraRecognizers
+import Mathlib.Data.Set.Basic
 
 #align_import linear_algebra.linear_independent from "leanprover-community/mathlib"@"9d684a893c52e1d6692a504a118bfccbae04feeb"

feat(LinearAlgebra/LinearIndependent): add linearIndependent_iff_finset_linearIndependent (#9797)

A family is linearly independent if and only if all of its finite subfamily is linearly independent.

4bb560b5

Diff

@@ -238,6 +238,14 @@ theorem LinearIndependent.comp (h : LinearIndependent R v) (f : ι' → ι) (hf
   rw [Finsupp.mapDomain_apply hf]
 #align linear_independent.comp LinearIndependent.comp
 
+/-- A family is linearly independent if and only if all of its finite subfamily is
+linearly independent. -/
+theorem linearIndependent_iff_finset_linearIndependent :
+    LinearIndependent R v ↔ ∀ (s : Finset ι), LinearIndependent R (v ∘ (Subtype.val : s → ι)) :=
+  ⟨fun H _ ↦ H.comp _ Subtype.val_injective, fun H ↦ linearIndependent_iff'.2 fun s g hg i hi ↦
+    Fintype.linearIndependent_iff.1 (H s) (g ∘ Subtype.val)
+      (hg ▸ Finset.sum_attach s fun j ↦ g j • v j) ⟨i, hi⟩⟩
+
 theorem LinearIndependent.coe_range (i : LinearIndependent R v) :
     LinearIndependent R ((↑) : range v → M) := by simpa using i.comp _ (rangeSplitting_injective v)
 #align linear_independent.coe_range LinearIndependent.coe_range

chore(*): rename FunLike to DFunLike (#9785)

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

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

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

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

82656743

Diff

@@ -144,7 +144,7 @@ theorem linearIndependent_iff' :
               (fun j _hjs hji => by rw [Finsupp.lapply_apply, Finsupp.single_eq_of_ne hji])
               fun hnis => hnis.elim his
         _ = (∑ j in s, Finsupp.single j (g j)) i := (map_sum ..).symm
-        _ = 0 := FunLike.ext_iff.1 h i,
+        _ = 0 := DFunLike.ext_iff.1 h i,
       fun hf l hl =>
       Finsupp.ext fun i =>
         _root_.by_contradiction fun hni => hni <| hf _ _ hl _ <| Finsupp.mem_support_iff.2 hni⟩
@@ -1204,7 +1204,7 @@ lemma linearIndependent_algHom_toLinearMap
   apply LinearIndependent.of_comp (LinearMap.ltoFun K M L)
   exact (linearIndependent_monoidHom M L).comp
     (RingHom.toMonoidHom ∘ AlgHom.toRingHom)
-    (fun _ _ e ↦ AlgHom.ext (FunLike.congr_fun e : _))
+    (fun _ _ e ↦ AlgHom.ext (DFunLike.congr_fun e : _))
 
 lemma linearIndependent_algHom_toLinearMap' (K M L) [CommRing K]
     [Semiring M] [Algebra K M] [CommRing L] [IsDomain L] [Algebra K L] [NoZeroSMulDivisors K L] :

chore(Function): rename some lemmas (#9738)

Merge Function.left_id and Function.comp.left_id into Function.id_comp.
Merge Function.right_id and Function.comp.right_id into Function.comp_id.
Merge Function.comp_const_right and Function.comp_const into Function.comp_const, use explicit arguments.
Move Function.const_comp to Mathlib.Init.Function, use explicit arguments.

87c10369

Diff

@@ -328,7 +328,7 @@ theorem linearIndependent_of_subsingleton [Subsingleton R] : LinearIndependent R
 
 theorem linearIndependent_equiv (e : ι ≃ ι') {f : ι' → M} :
     LinearIndependent R (f ∘ e) ↔ LinearIndependent R f :=
-  ⟨fun h => Function.comp.right_id f ▸ e.self_comp_symm ▸ h.comp _ e.symm.injective, fun h =>
+  ⟨fun h => Function.comp_id f ▸ e.self_comp_symm ▸ h.comp _ e.symm.injective, fun h =>
     h.comp _ e.injective⟩
 #align linear_independent_equiv linearIndependent_equiv

feat(LinearAlgebra): generalize results about Module.rank of LinearMap. (#9677)

LinearAlgebra/LinearIndependent: generalize linearIndependent_algHom_toLinearMap(') to allow different domain and codomain of the AlgHom.

LinearAlgebra/Basic: add LinearEquiv.congrLeft that works for two rings with commuting actions on the codomain.

LinearAlgebra/FreeModule/Finite/Matrix: generalize Module.Free.linearMap, Module.Finite.linearMap, and FiniteDimensional.finrank_linearMap to work with two different rings that may be noncommutative. Add FiniteDimensional.rank_linearMap, FiniteDimensional.(fin)rank_linearMap_self, and card/cardinal_mk_algHom_le_rank.

FieldTheory/Tower: remove the instance LinearMap.finite_dimensional'' which becomes redundant; mark finrank_linear_map' as deprecated (superseded by finrank_linearMap_self.

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

56178f0a

Diff

@@ -1199,17 +1199,17 @@ theorem linearIndependent_monoidHom (G : Type*) [Monoid G] (L : Type*) [CommRing
 #align linear_independent_monoid_hom linearIndependent_monoidHom
 
 lemma linearIndependent_algHom_toLinearMap
-    (K L) [CommSemiring K] [CommRing L] [IsDomain L] [Algebra K L] :
-    LinearIndependent L (AlgHom.toLinearMap : (L →ₐ[K] L) → L →ₗ[K] L) := by
-  apply LinearIndependent.of_comp (LinearMap.ltoFun K L L)
-  exact (linearIndependent_monoidHom L L).comp
+    (K M L) [CommSemiring K] [Semiring M] [Algebra K M] [CommRing L] [IsDomain L] [Algebra K L] :
+    LinearIndependent L (AlgHom.toLinearMap : (M →ₐ[K] L) → M →ₗ[K] L) := by
+  apply LinearIndependent.of_comp (LinearMap.ltoFun K M L)
+  exact (linearIndependent_monoidHom M L).comp
     (RingHom.toMonoidHom ∘ AlgHom.toRingHom)
     (fun _ _ e ↦ AlgHom.ext (FunLike.congr_fun e : _))
 
-lemma linearIndependent_algHom_toLinearMap'
-    (K L) [CommRing K] [CommRing L] [IsDomain L] [Algebra K L] [NoZeroSMulDivisors K L] :
-    LinearIndependent K (AlgHom.toLinearMap : (L →ₐ[K] L) → L →ₗ[K] L) := by
-  apply (linearIndependent_algHom_toLinearMap K L).restrict_scalars
+lemma linearIndependent_algHom_toLinearMap' (K M L) [CommRing K]
+    [Semiring M] [Algebra K M] [CommRing L] [IsDomain L] [Algebra K L] [NoZeroSMulDivisors K L] :
+    LinearIndependent K (AlgHom.toLinearMap : (M →ₐ[K] L) → M →ₗ[K] L) := by
+  apply (linearIndependent_algHom_toLinearMap K M L).restrict_scalars
   simp_rw [Algebra.smul_def, mul_one]
   exact NoZeroSMulDivisors.algebraMap_injective K L

chore(*): use ∃ x ∈ s, p x instead of ∃ x (_ : x ∈ s), p x (#9326)

This is a follow-up to #9215. It changes the following theorems and definitions:

IsOpen.exists_subset_affineIndependent_span_eq_top
IsConformalMap
SimpleGraph.induce_connected_of_patches
Submonoid.exists_list_of_mem_closure
AddSubmonoid.exists_list_of_mem_closure
AffineSubspace.mem_affineSpan_insert_iff
AffineBasis.exists_affine_subbasis
exists_affineIndependent
LinearMap.mem_submoduleImage
Basis.basis_singleton_iff
atom_iff_nonzero_span
finrank_eq_one_iff'
Submodule.basis_of_pid_aux
exists_linearIndependent_extension
exists_linearIndependent
countable_cover_nhdsWithin_of_sigma_compact
mem_residual

Also deprecate ENNReal.exists_ne_top'.

3d1cf78f

Diff

@@ -1396,7 +1396,7 @@ theorem linearIndependent_fin2 {f : Fin 2 → V} :
 #align linear_independent_fin2 linearIndependent_fin2
 
 theorem exists_linearIndependent_extension (hs : LinearIndependent K ((↑) : s → V)) (hst : s ⊆ t) :
-    ∃ (b : _) (_ : b ⊆ t), s ⊆ b ∧ t ⊆ span K b ∧ LinearIndependent K ((↑) : b → V) := by
+    ∃ b ⊆ t, s ⊆ b ∧ t ⊆ span K b ∧ LinearIndependent K ((↑) : b → V) := by
   -- Porting note: The placeholder should be solved before `rcases`.
   have := by
     refine zorn_subset_nonempty { b | b ⊆ t ∧ LinearIndependent K ((↑) : b → V) } ?_ _ ⟨hst, hs⟩
@@ -1416,7 +1416,7 @@ theorem exists_linearIndependent_extension (hs : LinearIndependent K ((↑) : s
 variable (K t)
 
 theorem exists_linearIndependent :
-    ∃ (b : _) (_ : b ⊆ t), span K b = span K t ∧ LinearIndependent K ((↑) : b → V) := by
+    ∃ b ⊆ t, span K b = span K t ∧ LinearIndependent K ((↑) : b → V) := by
   obtain ⟨b, hb₁, -, hb₂, hb₃⟩ :=
     exists_linearIndependent_extension (linearIndependent_empty K V) (Set.empty_subset t)
   exact ⟨b, hb₁, (span_eq_of_le _ hb₂ (Submodule.span_mono hb₁)).symm, hb₃⟩

chore(*): replace $ with <| (#9319)

See Zulip thread for the discussion.

9f6d3388

Diff

@@ -461,19 +461,19 @@ theorem linearIndependent_subtype {s : Set M} :
 
 theorem linearIndependent_comp_subtype_disjoint {s : Set ι} :
     LinearIndependent R (v ∘ (↑) : s → M) ↔
-      Disjoint (Finsupp.supported R R s) (LinearMap.ker $ Finsupp.total ι M R v) :=
+      Disjoint (Finsupp.supported R R s) (LinearMap.ker <| Finsupp.total ι M R v) :=
   by rw [linearIndependent_comp_subtype, LinearMap.disjoint_ker]
 #align linear_independent_comp_subtype_disjoint linearIndependent_comp_subtype_disjoint
 
 theorem linearIndependent_subtype_disjoint {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
-      Disjoint (Finsupp.supported R R s) (LinearMap.ker $ Finsupp.total M M R id) :=
+      Disjoint (Finsupp.supported R R s) (LinearMap.ker <| Finsupp.total M M R id) :=
   by apply linearIndependent_comp_subtype_disjoint (v := id)
 #align linear_independent_subtype_disjoint linearIndependent_subtype_disjoint
 
 theorem linearIndependent_iff_totalOn {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
-    (LinearMap.ker $ Finsupp.totalOn M M R id s) = ⊥ := by
+    (LinearMap.ker <| Finsupp.totalOn M M R id s) = ⊥ := by
   rw [Finsupp.totalOn, LinearMap.ker, LinearMap.comap_codRestrict, Submodule.map_bot, comap_bot,
     LinearMap.ker_comp, linearIndependent_subtype_disjoint, disjoint_iff_inf_le, ←
     map_comap_subtype, map_le_iff_le_comap, comap_bot, ker_subtype, le_bot_iff]

feat: Cyclic extensions are kummer. (#9368)

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

39e97562

Diff

@@ -1198,6 +1198,21 @@ theorem linearIndependent_monoidHom (G : Type*) [Monoid G] (L : Type*) [CommRing
         (Finset.forall_mem_insert ..).2 ⟨h4, h3⟩
 #align linear_independent_monoid_hom linearIndependent_monoidHom
 
+lemma linearIndependent_algHom_toLinearMap
+    (K L) [CommSemiring K] [CommRing L] [IsDomain L] [Algebra K L] :
+    LinearIndependent L (AlgHom.toLinearMap : (L →ₐ[K] L) → L →ₗ[K] L) := by
+  apply LinearIndependent.of_comp (LinearMap.ltoFun K L L)
+  exact (linearIndependent_monoidHom L L).comp
+    (RingHom.toMonoidHom ∘ AlgHom.toRingHom)
+    (fun _ _ e ↦ AlgHom.ext (FunLike.congr_fun e : _))
+
+lemma linearIndependent_algHom_toLinearMap'
+    (K L) [CommRing K] [CommRing L] [IsDomain L] [Algebra K L] [NoZeroSMulDivisors K L] :
+    LinearIndependent K (AlgHom.toLinearMap : (L →ₐ[K] L) → L →ₗ[K] L) := by
+  apply (linearIndependent_algHom_toLinearMap K L).restrict_scalars
+  simp_rw [Algebra.smul_def, mul_one]
+  exact NoZeroSMulDivisors.algebraMap_injective K L
+
 theorem le_of_span_le_span [Nontrivial R] {s t u : Set M} (hl : LinearIndependent R ((↑) : u → M))
     (hsu : s ⊆ u) (htu : t ⊆ u) (hst : span R s ≤ span R t) : s ⊆ t := by
   have :=

chore: Improve Finset lemma names (#8894)

Change a few lemma names that have historically bothered me.

Finset.card_le_of_subset → Finset.card_le_card
Multiset.card_le_of_le → Multiset.card_le_card
Multiset.card_lt_of_lt → Multiset.card_lt_card
Set.ncard_le_of_subset → Set.ncard_le_ncard
Finset.image_filter → Finset.filter_image
CompleteLattice.finset_sup_compact_of_compact → CompleteLattice.isCompactElement_finset_sup

7d3d6e43

Diff

@@ -1516,7 +1516,7 @@ theorem exists_finite_card_le_of_finite_of_linearIndependent_of_span (ht : t.Fin
   have : s ⊆ (span K ↑ht.toFinset : Submodule K V) := by simp; assumption
   let ⟨u, _hust, hsu, Eq⟩ := exists_of_linearIndependent_of_finite_span hs this
   have : s.Finite := u.finite_toSet.subset hsu
-  ⟨this, by rw [← Eq]; exact Finset.card_le_of_subset <| Finset.coe_subset.mp <| by simp [hsu]⟩
+  ⟨this, by rw [← Eq]; exact Finset.card_le_card <| Finset.coe_subset.mp <| by simp [hsu]⟩
 #align exists_finite_card_le_of_finite_of_linear_independent_of_span exists_finite_card_le_of_finite_of_linearIndependent_of_span
 
 end Module

chore(*): use ∀ s ⊆ t, _ etc (#9276)

Changes in this PR shouldn't change the public API. The only changes about ∃ x ∈ s, _ is inside a proof.

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

be0b59d2

Diff

@@ -1005,7 +1005,7 @@ theorem exists_maximal_independent' (s : ι → M) :
 theorem exists_maximal_independent (s : ι → M) :
     ∃ I : Set ι,
       (LinearIndependent R fun x : I => s x) ∧
-        ∀ (i) (_ : i ∉ I), ∃ a : R, a ≠ 0 ∧ a • s i ∈ span R (s '' I) := by
+        ∀ i ∉ I, ∃ a : R, a ≠ 0 ∧ a • s i ∈ span R (s '' I) := by
   classical
     rcases exists_maximal_independent' R s with ⟨I, hIlinind, hImaximal⟩
     use I, hIlinind

feat(LinearAlgebra/Dimension): add various surjective_injective results (#9156)

Add various results concerning modules M / R and M' / R' with maps i : R -> R' and j : M -> M' which are compatible with scalar multiplications on M and M'.

if i : R' -> R is injective and j is injective, then:
- LinearIndependent.map_of_injective_injective: j preserves linear independent subsets.
- [lift_]rank_le_of_injective_injective: rank of M / R is smaller than or equal to the rank of M' / R'.
if i is surjective and j is injective, then:
- LinearIndependent.map_of_surjective_injective: j preserves linear independent subsets.
- [lift_]rank_le_of_surjective_injective: rank of M / R is smaller than or equal to the rank of M' / R'.
if i and j are both bijective, then [lift_]rank_eq_of_equiv_equiv: rank of M / R is equal to the rank of M' / R'.

Also add the Algebra versions of these results.

98067b25

Diff

@@ -275,6 +275,35 @@ theorem LinearIndependent.map' (hv : LinearIndependent R v) (f : M →ₗ[R] M')
   hv.map <| by simp [hf_inj]
 #align linear_independent.map' LinearIndependent.map'
 
+/-- If `M / R` and `M' / R'` are modules, `i : R' → R` is a map, `j : M →+ M'` is a monoid map,
+such that they send non-zero elements to non-zero elements, and compatible with the scalar
+multiplications on `M` and `M'`, then `j` sends linearly independent families of vectors to
+linearly independent families of vectors. As a special case, taking `R = R'`
+it is `LinearIndependent.map'`. -/
+theorem LinearIndependent.map_of_injective_injective {R' : Type*} {M' : Type*}
+    [Semiring R'] [AddCommMonoid M'] [Module R' M'] (hv : LinearIndependent R v)
+    (i : R' → R) (j : M →+ M') (hi : ∀ r, i r = 0 → r = 0) (hj : ∀ m, j m = 0 → m = 0)
+    (hc : ∀ (r : R') (m : M), j (i r • m) = r • j m) : LinearIndependent R' (j ∘ v) := by
+  rw [linearIndependent_iff'] at hv ⊢
+  intro S r' H s hs
+  simp_rw [comp_apply, ← hc, ← map_sum] at H
+  exact hi _ <| hv _ _ (hj _ H) s hs
+
+/-- If `M / R` and `M' / R'` are modules, `i : R → R'` is a surjective map which maps zero to zero,
+`j : M →+ M'` is a monoid map which sends non-zero elements to non-zero elements, such that the
+scalar multiplications on `M` and `M'` are compatible, then `j` sends linearly independent families
+of vectors to linearly independent families of vectors. As a special case, taking `R = R'`
+it is `LinearIndependent.map'`. -/
+theorem LinearIndependent.map_of_surjective_injective {R' : Type*} {M' : Type*}
+    [Semiring R'] [AddCommMonoid M'] [Module R' M'] (hv : LinearIndependent R v)
+    (i : ZeroHom R R') (j : M →+ M') (hi : Surjective i) (hj : ∀ m, j m = 0 → m = 0)
+    (hc : ∀ (r : R) (m : M), j (r • m) = i r • j m) : LinearIndependent R' (j ∘ v) := by
+  obtain ⟨i', hi'⟩ := hi.hasRightInverse
+  refine hv.map_of_injective_injective i' j (fun _ h ↦ ?_) hj fun r m ↦ ?_
+  · apply_fun i at h
+    rwa [hi', i.map_zero] at h
+  rw [hc (i' r) m, hi']
+
 /-- If the image of a family of vectors under a linear map is linearly independent, then so is
 the original family. -/
 theorem LinearIndependent.of_comp (f : M →ₗ[R] M') (hfv : LinearIndependent R (f ∘ v)) :

chore(*): use ∃ x ∈ s, _ instead of ∃ (x) (_ : x ∈ s), _ (#9184)

Search for [∀∃].*(_ and manually replace some occurrences with more readable versions. In case of ∀, the new expressions are defeq to the old ones. In case of ∃, they differ by exists_prop.

In some rare cases, golf proofs that needed fixing.

14c72960

Diff

@@ -152,7 +152,7 @@ theorem linearIndependent_iff' :
 
 theorem linearIndependent_iff'' :
     LinearIndependent R v ↔
-      ∀ (s : Finset ι) (g : ι → R) (_hg : ∀ (i) (_ : i ∉ s), g i = 0),
+      ∀ (s : Finset ι) (g : ι → R), (∀ i ∉ s, g i = 0) →
         ∑ i in s, g i • v i = 0 → ∀ i, g i = 0 := by
   classical
   exact linearIndependent_iff'.trans
@@ -470,7 +470,7 @@ theorem LinearIndependent.mono {t s : Set M} (h : t ⊆ s) :
 #align linear_independent.mono LinearIndependent.mono
 
 theorem linearIndependent_of_finite (s : Set M)
-    (H : ∀ (t) (_ : t ⊆ s), Set.Finite t → LinearIndependent R (fun x => x : t → M)) :
+    (H : ∀ t ⊆ s, Set.Finite t → LinearIndependent R (fun x => x : t → M)) :
     LinearIndependent R (fun x => x : s → M) :=
   linearIndependent_subtype.2 fun l hl =>
     linearIndependent_subtype.1 (H _ hl (Finset.finite_toSet _)) l (Subset.refl _)

refactor: replace some [@foo](https://github.com/foo) _ _ _ _ _ ... by named arguments (#8702)

Using Lean4's named arguments, we manage to remove a few hard-to-read explicit function calls [@foo](https://github.com/foo) _ _ _ _ _ ... which used to be necessary in Lean3.

Occasionally, this results in slightly longer code. The benefit of named arguments is readability, as well as to reduce the brittleness of the code when the argument order is changed.

Co-authored-by: Michael Rothgang <rothgami@math.hu-berlin.de>

df634f2a

Diff

@@ -253,7 +253,7 @@ theorem LinearIndependent.map (hv : LinearIndependent R v) {f : M →ₗ[R] M'}
   unfold LinearIndependent at hv ⊢
   rw [hv, le_bot_iff] at hf_inj
   haveI : Inhabited M := ⟨0⟩
-  rw [Finsupp.total_comp, @Finsupp.lmapDomain_total _ _ R _ _ _ _ _ _ _ _ _ _ f, LinearMap.ker_comp,
+  rw [Finsupp.total_comp, Finsupp.lmapDomain_total _ _ f, LinearMap.ker_comp,
     hf_inj]
   exact fun _ => rfl
 #align linear_independent.map LinearIndependent.map
@@ -322,8 +322,8 @@ theorem linearIndependent_image {ι} {s : Set ι} {f : ι → M} (hf : Set.InjOn
 #align linear_independent_image linearIndependent_image
 
 theorem linearIndependent_span (hs : LinearIndependent R v) :
-    @LinearIndependent ι R (span R (range v)) (fun i : ι => ⟨v i, subset_span (mem_range_self i)⟩) _
-      _ _ :=
+    LinearIndependent R (M := span R (range v))
+      (fun i : ι => ⟨v i, subset_span (mem_range_self i)⟩) :=
   LinearIndependent.of_comp (span R (range v)).subtype hs
 #align linear_independent_span linearIndependent_span
 
@@ -427,7 +427,7 @@ theorem linearDependent_comp_subtype {s : Set ι} :
 theorem linearIndependent_subtype {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
       ∀ l ∈ Finsupp.supported R R s, (Finsupp.total M M R id) l = 0 → l = 0 :=
-  by apply @linearIndependent_comp_subtype _ _ _ id
+  by apply linearIndependent_comp_subtype (v := id)
 #align linear_independent_subtype linearIndependent_subtype
 
 theorem linearIndependent_comp_subtype_disjoint {s : Set ι} :
@@ -439,7 +439,7 @@ theorem linearIndependent_comp_subtype_disjoint {s : Set ι} :
 theorem linearIndependent_subtype_disjoint {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
       Disjoint (Finsupp.supported R R s) (LinearMap.ker $ Finsupp.total M M R id) :=
-  by apply @linearIndependent_comp_subtype_disjoint _ _ _ id
+  by apply linearIndependent_comp_subtype_disjoint (v := id)
 #align linear_independent_subtype_disjoint linearIndependent_subtype_disjoint
 
 theorem linearIndependent_iff_totalOn {s : Set M} :
@@ -649,7 +649,7 @@ theorem LinearIndependent.maximal_iff {ι : Type w} {R : Type u} [Ring R] [Nontr
   constructor
   · rintro p κ w i' j rfl
     specialize p (range w) i'.coe_range (range_comp_subset_range _ _)
-    rw [range_comp, ← @image_univ _ _ w] at p
+    rw [range_comp, ← image_univ (f := w)] at p
     exact range_iff_surjective.mp (image_injective.mpr i'.injective p)
   · intro p w i' h
     specialize
@@ -676,7 +676,7 @@ theorem LinearIndependent.eq_of_smul_apply_eq_smul_apply {M : Type*} [AddCommGro
   have h_single_eq : Finsupp.single i c = Finsupp.single j d := by
     rw [linearIndependent_iff] at li
     simp [eq_add_of_sub_eq' (li l h_total)]
-  rcases (Finsupp.single_eq_single_iff _ _ _ _).mp h_single_eq with (⟨H, _⟩ | ⟨hc, _⟩)
+  rcases (Finsupp.single_eq_single_iff ..).mp h_single_eq with (⟨H, _⟩ | ⟨hc, _⟩)
   · exact H
   · contradiction
 #align linear_independent.eq_of_smul_apply_eq_smul_apply LinearIndependent.eq_of_smul_apply_eq_smul_apply
@@ -968,7 +968,7 @@ theorem exists_maximal_independent' (s : ι → M) :
     exact linearIndependent_comp_subtype.mp I.2 f hI hsum
   have trans : Transitive r := fun I J K => Set.Subset.trans
   obtain ⟨⟨I, hli : indep I⟩, hmax : ∀ a, r ⟨I, hli⟩ a → r a ⟨I, hli⟩⟩ :=
-    @exists_maximal_of_chains_bounded _ r
+    exists_maximal_of_chains_bounded
       (fun c hc => ⟨⟨⋃ I ∈ c, (I : Set ι), key c hc⟩, fun I => Set.subset_biUnion_of_mem⟩) @trans
   exact ⟨I, hli, fun J hsub hli => Set.Subset.antisymm hsub (hmax ⟨J, hli⟩ hsub)⟩
 #align exists_maximal_independent' exists_maximal_independent'
@@ -1052,7 +1052,7 @@ theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
     (hs : LinearIndependent R (fun x => x : s → M))
     (hf_inj : Disjoint (span R s) (LinearMap.ker f)) :
     LinearIndependent R (fun x => x : f '' s → M') := by
-  rw [← @Subtype.range_coe _ s] at hf_inj
+  rw [← Subtype.range_coe (s := s)] at hf_inj
   refine' (hs.map hf_inj).to_subtype_range' _
   simp [Set.range_comp f]
 #align linear_independent.image_subtype LinearIndependent.image_subtype
@@ -1078,7 +1078,7 @@ theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv :
 --  <https://kconrad.math.uconn.edu/blurbs/galoistheory/linearchar.pdf>
 /-- Dedekind's linear independence of characters -/
 theorem linearIndependent_monoidHom (G : Type*) [Monoid G] (L : Type*) [CommRing L]
-    [NoZeroDivisors L] : @LinearIndependent _ L (G → L) (fun f => f : (G →* L) → G → L) _ _ _ := by
+    [NoZeroDivisors L] : LinearIndependent L (M := G → L) (fun f => f : (G →* L) → G → L) := by
   -- Porting note: Some casts are required.
   letI := Classical.decEq (G →* L);
   letI : MulAction L L := DistribMulAction.toMulAction;
@@ -1107,9 +1107,9 @@ theorem linearIndependent_monoidHom (G : Type*) [Monoid G] (L : Type*) [CommRing
                 -- After that, it's just a chase scene.
                 (∑ i in s, ((g i * i x - g i * a x) • (i : G → L))) y =
                     ∑ i in s, (g i * i x - g i * a x) * i y :=
-                  Finset.sum_apply _ _ _
+                  Finset.sum_apply ..
                 _ = ∑ i in s, (g i * i x * i y - g i * a x * i y) :=
-                  Finset.sum_congr rfl fun _ _ => sub_mul _ _ _
+                  Finset.sum_congr rfl fun _ _ => sub_mul ..
                 _ = (∑ i in s, g i * i x * i y) - ∑ i in s, g i * a x * i y :=
                   Finset.sum_sub_distrib
                 _ =
@@ -1166,7 +1166,7 @@ theorem linearIndependent_monoidHom (G : Type*) [Monoid G] (L : Type*) [CommRing
             _ = 0 := by rw [hg]; rfl
         -- Now we're done; the last two facts together imply that `g` vanishes on every element
         -- of `insert a s`.
-        (Finset.forall_mem_insert _ _ _).2 ⟨h4, h3⟩
+        (Finset.forall_mem_insert ..).2 ⟨h4, h3⟩
 #align linear_independent_monoid_hom linearIndependent_monoidHom
 
 theorem le_of_span_le_span [Nontrivial R] {s t u : Set M} (hl : LinearIndependent R ((↑) : u → M))
@@ -1299,7 +1299,7 @@ theorem linearIndependent_insert' {ι} {s : Set ι} {a : ι} {f : ι → V} (has
 theorem linearIndependent_insert (hxs : x ∉ s) :
     (LinearIndependent K fun b : ↥(insert x s) => (b : V)) ↔
       (LinearIndependent K fun b : s => (b : V)) ∧ x ∉ Submodule.span K s :=
-  (@linearIndependent_insert' _ _ _ _ _ _ _ _ id hxs).trans <| by simp
+  (linearIndependent_insert' (f := id) hxs).trans <| by simp
 #align linear_independent_insert linearIndependent_insert
 
 theorem linearIndependent_pair {x y : V} (hx : x ≠ 0) (hy : ∀ a : K, a • x ≠ y) :

feat: analysis delaborator for LinearIndependent (#8602)

This is an experimental delaborator that works by analyzing the expression and tagging it with pp.analysis-style hints.

This causes pretty printing LinearIndependent like LinearIndependent K fun (b : ↑s) ↦ ↑b rather than LinearIndependent K fun b ↦ ↑b and LinearIndependent (ι := { x // x ∈ s }) K Subtype.val rather than LinearIndependent K Subtype.val.

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

c26fbb12

Diff

@@ -9,6 +9,7 @@ import Mathlib.LinearAlgebra.Prod
 import Mathlib.SetTheory.Cardinal.Basic
 import Mathlib.Tactic.FinCases
 import Mathlib.Tactic.LinearCombination
+import Mathlib.Lean.Expr.ExtraRecognizers
 
 #align_import linear_algebra.linear_independent from "leanprover-community/mathlib"@"9d684a893c52e1d6692a504a118bfccbae04feeb"
 
@@ -100,6 +101,26 @@ def LinearIndependent : Prop :=
   LinearMap.ker (Finsupp.total ι M R v) = ⊥
 #align linear_independent LinearIndependent
 
+open Lean PrettyPrinter.Delaborator SubExpr in
+/-- Delaborator for `LinearIndependent` that suggests pretty printing with type hints
+in case the family of vectors is over a `Set`.
+
+Type hints look like `LinearIndependent fun (v : ↑s) => ↑v` or `LinearIndependent (ι := ↑s) f`,
+depending on whether the family is a lambda expression or not. -/
+@[delab app.LinearIndependent]
+def delabLinearIndependent : Delab :=
+  whenPPOption getPPNotation <|
+  whenNotPPOption getPPAnalysisSkip <|
+  withOptionAtCurrPos `pp.analysis.skip true do
+    let e ← getExpr
+    guard <| e.isAppOfArity ``LinearIndependent 7
+    let some _ := (e.getArg! 0).coeTypeSet? | failure
+    let optionsPerPos ← if (e.getArg! 3).isLambda then
+      withNaryArg 3 do return (← read).optionsPerPos.setBool (← getPos) pp.funBinderTypes.name true
+    else
+      withNaryArg 0 do return (← read).optionsPerPos.setBool (← getPos) `pp.analysis.namedArg true
+    withTheReader Context ({· with optionsPerPos}) delab
+
 variable {R} {v}
 
 theorem linearIndependent_iff : LinearIndependent R v ↔ ∀ l, Finsupp.total ι M R v l = 0 → l = 0 :=

feat: generalize some lemmas to directed types (#7852)

New lemmas / instances

An archimedean ordered semiring is directed upwards.
Filter.hasAntitoneBasis_atTop;
Filter.HasAntitoneBasis.iInf_principal;

Fix typos

Docstrings: "if the agree" -> "if they agree".
ProbabilityTheory.measure_eq_zero_or_one_of_indepSetCat_self -> ProbabilityTheory.measure_eq_zero_or_one_of_indepSet_self.

Weaken typeclass assumptions

From a semilattice to a directed type

MeasureTheory.tendsto_measure_iUnion;
MeasureTheory.tendsto_measure_iInter;
Monotone.directed_le, Monotone.directed_ge;
Antitone.directed_le, Antitone.directed_ge;
directed_of_sup, renamed to directed_of_isDirected_le;
directed_of_inf, renamed to directed_of_isDirected_ge;

From a strict ordered semiring to an ordered semiring

tendsto_nat_cast_atTop_atTop;
Filter.Eventually.nat_cast_atTop;
atTop_hasAntitoneBasis_of_archimedean;

65b7d164

Diff

@@ -756,7 +756,7 @@ theorem linearIndependent_iUnion_finite_subtype {ι : Type*} {f : ι → Set M}
   classical
   rw [iUnion_eq_iUnion_finset f]
   apply linearIndependent_iUnion_of_directed
-  · apply directed_of_sup
+  · apply directed_of_isDirected_le
     exact fun t₁ t₂ ht => iUnion_mono fun i => iUnion_subset_iUnion_const fun h => ht h
   intro t
   induction' t using Finset.induction_on with i s his ih

chore: use _root_.map_sum more consistently (#7189)

Also _root_.map_smul when in the neighbourhood.

1fa13fb0

Diff

@@ -113,7 +113,7 @@ theorem linearIndependent_iff' :
     ⟨fun hf s g hg i his =>
       have h :=
         hf (∑ i in s, Finsupp.single i (g i)) <| by
-          simpa only [LinearMap.map_sum, Finsupp.total_single] using hg
+          simpa only [map_sum, Finsupp.total_single] using hg
       calc
         g i = (Finsupp.lapply i : (ι →₀ R) →ₗ[R] R) (Finsupp.single i (g i)) := by
           { rw [Finsupp.lapply_apply, Finsupp.single_eq_same] }
@@ -122,10 +122,8 @@ theorem linearIndependent_iff' :
             Finset.sum_eq_single i
               (fun j _hjs hji => by rw [Finsupp.lapply_apply, Finsupp.single_eq_of_ne hji])
               fun hnis => hnis.elim his
-        _ = (∑ j in s, Finsupp.single j (g j)) i :=
-          (Finsupp.lapply i : (ι →₀ R) →ₗ[R] R).map_sum.symm
-        _ = 0 := FunLike.ext_iff.1 h i
-        ,
+        _ = (∑ j in s, Finsupp.single j (g j)) i := (map_sum ..).symm
+        _ = 0 := FunLike.ext_iff.1 h i,
       fun hf l hl =>
       Finsupp.ext fun i =>
         _root_.by_contradiction fun hni => hni <| hf _ _ hl _ <| Finsupp.mem_support_iff.2 hni⟩
@@ -262,7 +260,7 @@ theorem LinearIndependent.of_comp (f : M →ₗ[R] M') (hfv : LinearIndependent
     LinearIndependent R v :=
   linearIndependent_iff'.2 fun s g hg i his =>
     have : (∑ i : ι in s, g i • f (v i)) = 0 := by
-      simp_rw [← f.map_smul, ← f.map_sum, hg, f.map_zero]
+      simp_rw [← map_smul, ← map_sum, hg, f.map_zero]
     linearIndependent_iff'.1 hfv s g this i his
 #align linear_independent.of_comp LinearIndependent.of_comp

feat: the complement of a countable set is path-connected in dimension > 1 (#6690)

Also show that spheres are path-connected in dimension > 1.

23550c1e

Diff

@@ -7,6 +7,8 @@ import Mathlib.Algebra.BigOperators.Fin
 import Mathlib.LinearAlgebra.Finsupp
 import Mathlib.LinearAlgebra.Prod
 import Mathlib.SetTheory.Cardinal.Basic
+import Mathlib.Tactic.FinCases
+import Mathlib.Tactic.LinearCombination
 
 #align_import linear_algebra.linear_independent from "leanprover-community/mathlib"@"9d684a893c52e1d6692a504a118bfccbae04feeb"
 
@@ -194,6 +196,16 @@ lemma LinearIndependent.eq_zero_of_pair {x y : M} (h : LinearIndependent R ![x,
     Finset.mem_univ, forall_true_left] at this
   exact ⟨this 0, this 1⟩
 
+lemma LinearIndependent.pair_iff {x y : M} :
+    LinearIndependent R ![x, y] ↔ ∀ (s t : R), s • x + t • y = 0 → s = 0 ∧ t = 0 := by
+  refine ⟨fun h s t hst ↦ h.eq_zero_of_pair hst, fun h ↦ ?_⟩
+  apply Fintype.linearIndependent_iff.2
+  intro g hg
+  simp only [Fin.sum_univ_two, Matrix.cons_val_zero, Matrix.cons_val_one, Matrix.head_cons] at hg
+  intro i
+  fin_cases i
+  exacts [(h _ _ hg).1, (h _ _ hg).2]
+
 /-- A subfamily of a linearly independent family (i.e., a composition with an injective map) is a
 linearly independent family. -/
 theorem LinearIndependent.comp (h : LinearIndependent R v) (f : ι' → ι) (hf : Injective f) :
@@ -571,6 +583,29 @@ lemma LinearIndependent.eq_of_pair {x y : M} (h : LinearIndependent R ![x, y])
     abel
   simpa [sub_eq_zero] using h.eq_zero_of_pair this
 
+lemma LinearIndependent.eq_zero_of_pair' {x y : M} (h : LinearIndependent R ![x, y])
+    {s t : R} (h' : s • x = t • y) : s = 0 ∧ t = 0 := by
+  suffices H : s = 0 ∧ 0 = t from ⟨H.1, H.2.symm⟩
+  exact h.eq_of_pair (by simpa using h')
+
+/-- If two vectors `x` and `y` are linearly independent, so are their linear combinations
+`a x + b y` and `c x + d y` provided the determinant `a * d - b * c` is nonzero. -/
+lemma LinearIndependent.linear_combination_pair_of_det_ne_zero {R M : Type*} [CommRing R]
+    [NoZeroDivisors R] [AddCommGroup M] [Module R M]
+    {x y : M} (h : LinearIndependent R ![x, y])
+    {a b c d : R} (h' : a * d - b * c ≠ 0) :
+    LinearIndependent R ![a • x + b • y, c • x + d • y] := by
+  apply LinearIndependent.pair_iff.2 (fun s t hst ↦ ?_)
+  have H : (s * a + t * c) • x + (s * b + t * d) • y = 0 := by
+    convert hst using 1
+    simp only [_root_.add_smul, smul_add, smul_smul]
+    abel
+  have I1 : s * a + t * c = 0 := (h.eq_zero_of_pair H).1
+  have I2 : s * b + t * d = 0 := (h.eq_zero_of_pair H).2
+  have J1 : (a * d - b * c) * s = 0 := by linear_combination d * I1 - c * I2
+  have J2 : (a * d - b * c) * t = 0 := by linear_combination -b * I1 + a * I2
+  exact ⟨by simpa [h'] using mul_eq_zero.1 J1, by simpa [h'] using mul_eq_zero.1 J2⟩
+
 section Maximal
 
 universe v w

feat: patch for new alias command (#6172)

19e0ba92

Diff

@@ -282,7 +282,7 @@ theorem linearIndependent_subtype_range {ι} {f : ι → M} (hf : Injective f) :
   Iff.symm <| linearIndependent_equiv' (Equiv.ofInjective f hf) rfl
 #align linear_independent_subtype_range linearIndependent_subtype_range
 
-alias linearIndependent_subtype_range ↔ LinearIndependent.of_subtype_range _
+alias ⟨LinearIndependent.of_subtype_range, _⟩ := linearIndependent_subtype_range
 #align linear_independent.of_subtype_range LinearIndependent.of_subtype_range
 
 theorem linearIndependent_image {ι} {s : Set ι} {f : ι → M} (hf : Set.InjOn f s) :
@@ -494,7 +494,7 @@ theorem linearIndependent_iff_injective_total :
     (injective_iff_map_eq_zero (Finsupp.total ι M R v).toAddMonoidHom).symm
 #align linear_independent_iff_injective_total linearIndependent_iff_injective_total
 
-alias linearIndependent_iff_injective_total ↔ LinearIndependent.injective_total _
+alias ⟨LinearIndependent.injective_total, _⟩ := linearIndependent_iff_injective_total
 #align linear_independent.injective_total LinearIndependent.injective_total
 
 theorem LinearIndependent.injective [Nontrivial R] (hv : LinearIndependent R v) : Injective v := by
@@ -1146,7 +1146,7 @@ theorem linearIndependent_unique_iff (v : ι → M) [Unique ι] :
   exact one_ne_zero (Finsupp.single_eq_zero.1 this)
 #align linear_independent_unique_iff linearIndependent_unique_iff
 
-alias linearIndependent_unique_iff ↔ _ linearIndependent_unique
+alias ⟨_, linearIndependent_unique⟩ := linearIndependent_unique_iff
 #align linear_independent_unique linearIndependent_unique
 
 theorem linearIndependent_singleton {x : M} (hx : x ≠ 0) :

feat(LinearAlgebra): complements on spaces of dimension >1 or >n (#6348)

1a978e5c

Diff

@@ -187,6 +187,13 @@ theorem LinearIndependent.ne_zero [Nontrivial R] (i : ι) (hv : LinearIndependen
         · simp [h])
 #align linear_independent.ne_zero LinearIndependent.ne_zero
 
+lemma LinearIndependent.eq_zero_of_pair {x y : M} (h : LinearIndependent R ![x, y])
+    {s t : R} (h' : s • x + t • y = 0) : s = 0 ∧ t = 0 := by
+  have := linearIndependent_iff'.1 h Finset.univ ![s, t]
+  simp only [Fin.sum_univ_two, Matrix.cons_val_zero, Matrix.cons_val_one, Matrix.head_cons, h',
+    Finset.mem_univ, forall_true_left] at this
+  exact ⟨this 0, this 1⟩
+
 /-- A subfamily of a linearly independent family (i.e., a composition with an injective map) is a
 linearly independent family. -/
 theorem LinearIndependent.comp (h : LinearIndependent R v) (f : ι' → ι) (hf : Injective f) :
@@ -556,6 +563,14 @@ theorem LinearIndependent.units_smul {v : ι → M} (hv : LinearIndependent R v)
     rfl
 #align linear_independent.units_smul LinearIndependent.units_smul
 
+lemma LinearIndependent.eq_of_pair {x y : M} (h : LinearIndependent R ![x, y])
+    {s t s' t' : R} (h' : s • x + t • y = s' • x + t' • y) : s = s' ∧ t = t' := by
+  have : (s - s') • x + (t - t') • y = 0 := by
+    rw [← sub_eq_zero_of_eq h', ← sub_eq_zero]
+    simp only [sub_smul]
+    abel
+  simpa [sub_eq_zero] using h.eq_zero_of_pair this
+
 section Maximal
 
 universe v w

chore: golf some proofs introduced in #6360 (#6405)

Notably, getting rid of some injectivity restrictions makes some later proofs simpler.

Co-authored-by: dagurtomas <dagurtomas@gmail.com> Co-authored-by: Dagur Tómas Ásgeirsson <dagurtomas@gmail.com>

280a9f50

Diff

@@ -222,35 +222,13 @@ theorem LinearIndependent.map (hv : LinearIndependent R v) {f : M →ₗ[R] M'}
 
 /-- If `v` is an injective family of vectors such that `f ∘ v` is linearly independent, then `v`
     spans a submodule disjoint from the kernel of `f` -/
-theorem Submodule.ker_range_disjoint {f : M →ₗ[R] M'} (hi : v.Injective)
+theorem Submodule.range_ker_disjoint {f : M →ₗ[R] M'}
     (hv : LinearIndependent R (f ∘ v)) :
-    Disjoint (LinearMap.ker f) (Submodule.span R (Set.range v)) := by
-  rw [Submodule.disjoint_def]
-  intro m hm hmr
-  simp only [LinearMap.mem_ker] at hm
-  rw [mem_span_set] at hmr
-  obtain ⟨c, ⟨hc, hsum⟩⟩ := hmr
-  rw [← hsum, map_finsupp_sum] at hm
-  simp_rw [f.map_smul] at hm
-  dsimp [Finsupp.sum] at hm
-  rw [linearIndependent_iff'] at hv
-  specialize hv (Finset.preimage c.support v (Set.injOn_of_injective hi _))
-  rw [← Finset.sum_preimage v c.support (Set.injOn_of_injective hi _) _ _] at hm
-  · rw [← hsum]
-    apply Finset.sum_eq_zero
-    intro x hx
-    obtain ⟨y, hy⟩ := hc hx
-    rw [← hy]
-    have : c (v y) = 0
-    · apply hv (c ∘ v) hm y
-      simp only [Finset.mem_preimage, Function.comp_apply]
-      dsimp at hy
-      rwa [hy]
-    rw [this]
-    simp only [zero_smul]
-  · intro x hx hnx
-    exfalso
-    exact hnx (hc hx)
+    Disjoint (span R (range v)) (LinearMap.ker f) := by
+  rw [LinearIndependent, Finsupp.total_comp, Finsupp.lmapDomain_total R _ f (fun _ ↦ rfl),
+    LinearMap.ker_comp] at hv
+  rw [disjoint_iff_inf_le, ← Set.image_univ, Finsupp.span_image_eq_map_total,
+    map_inf_eq_map_inf_comap, hv, inf_bot_eq, map_bot]
 
 /-- An injective linear map sends linearly independent families of vectors to linearly independent
 families of vectors. See also `LinearIndependent.map` for a more general statement. -/

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

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

This has nice performance benefits.

32de3f67

Diff

@@ -26,7 +26,7 @@ linear combinations.
 
 ## Main definitions
 All definitions are given for families of vectors, i.e. `v : ι → M` where `M` is the module or
-vector space and `ι : Type _` is an arbitrary indexing type.
+vector space and `ι : Type*` is an arbitrary indexing type.
 
 * `LinearIndependent R v` states that the elements of the family `v` are linearly independent.
 
@@ -81,8 +81,8 @@ open BigOperators Cardinal
 
 universe u' u
 
-variable {ι : Type u'} {ι' : Type _} {R : Type _} {K : Type _}
-variable {M : Type _} {M' M'' : Type _} {V : Type u} {V' : Type _}
+variable {ι : Type u'} {ι' : Type*} {R : Type*} {K : Type*}
+variable {M : Type*} {M' M'' : Type*} {V : Type u} {V' : Type*}
 
 section Module
 
@@ -460,7 +460,7 @@ theorem linearIndependent_of_finite (s : Set M)
     linearIndependent_subtype.1 (H _ hl (Finset.finite_toSet _)) l (Subset.refl _)
 #align linear_independent_of_finite linearIndependent_of_finite
 
-theorem linearIndependent_iUnion_of_directed {η : Type _} {s : η → Set M} (hs : Directed (· ⊆ ·) s)
+theorem linearIndependent_iUnion_of_directed {η : Type*} {s : η → Set M} (hs : Directed (· ⊆ ·) s)
     (h : ∀ i, LinearIndependent R (fun x => x : s i → M)) :
     LinearIndependent R (fun x => x : (⋃ i, s i) → M) := by
   by_cases hη : Nonempty η
@@ -548,7 +548,7 @@ theorem LinearIndependent.image {ι} {s : Set ι} {f : ι → M}
   by convert LinearIndependent.image_of_comp s f id hs
 #align linear_independent.image LinearIndependent.image
 
-theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulAction G R]
+theorem LinearIndependent.group_smul {G : Type*} [hG : Group G] [DistribMulAction G R]
     [DistribMulAction G M] [IsScalarTower G R M] [SMulCommClass G R M] {v : ι → M}
     (hv : LinearIndependent R v) (w : ι → G) : LinearIndependent R (w • v) := by
   rw [linearIndependent_iff''] at hv ⊢
@@ -619,7 +619,7 @@ theorem LinearIndependent.maximal_iff {ι : Type w} {R : Type u} [Ring R] [Nontr
 end Maximal
 
 /-- Linear independent families are injective, even if you multiply either side. -/
-theorem LinearIndependent.eq_of_smul_apply_eq_smul_apply {M : Type _} [AddCommGroup M] [Module R M]
+theorem LinearIndependent.eq_of_smul_apply_eq_smul_apply {M : Type*} [AddCommGroup M] [Module R M]
     {v : ι → M} (li : LinearIndependent R v) (c d : R) (i j : ι) (hc : c ≠ 0)
     (h : c • v i = d • v j) : i = j := by
   let l : ι →₀ R := Finsupp.single i c - Finsupp.single j d
@@ -723,7 +723,7 @@ theorem LinearIndependent.union {s t : Set M} (hs : LinearIndependent R (fun x =
   (hs.sum_type ht <| by simpa).to_subtype_range' <| by simp
 #align linear_independent.union LinearIndependent.union
 
-theorem linearIndependent_iUnion_finite_subtype {ι : Type _} {f : ι → Set M}
+theorem linearIndependent_iUnion_finite_subtype {ι : Type*} {f : ι → Set M}
     (hl : ∀ i, LinearIndependent R (fun x => x : f i → M))
     (hd : ∀ i, ∀ t : Set ι, t.Finite → i ∉ t → Disjoint (span R (f i)) (⨆ i ∈ t, span R (f i))) :
     LinearIndependent R (fun x => x : (⋃ i, f i) → M) := by
@@ -742,7 +742,7 @@ theorem linearIndependent_iUnion_finite_subtype {ι : Type _} {f : ι → Set M}
     exact hd i s s.finite_toSet his
 #align linear_independent_Union_finite_subtype linearIndependent_iUnion_finite_subtype
 
-theorem linearIndependent_iUnion_finite {η : Type _} {ιs : η → Type _} {f : ∀ j : η, ιs j → M}
+theorem linearIndependent_iUnion_finite {η : Type*} {ιs : η → Type*} {f : ∀ j : η, ιs j → M}
     (hindep : ∀ j, LinearIndependent R (f j))
     (hd : ∀ i, ∀ t : Set η,
       t.Finite → i ∉ t → Disjoint (span R (range (f i))) (⨆ i ∈ t, span R (range (f i)))) :
@@ -1030,7 +1030,7 @@ theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv :
 -- See, for example, Keith Conrad's note
 --  <https://kconrad.math.uconn.edu/blurbs/galoistheory/linearchar.pdf>
 /-- Dedekind's linear independence of characters -/
-theorem linearIndependent_monoidHom (G : Type _) [Monoid G] (L : Type _) [CommRing L]
+theorem linearIndependent_monoidHom (G : Type*) [Monoid G] (L : Type*) [CommRing L]
     [NoZeroDivisors L] : @LinearIndependent _ L (G → L) (fun f => f : (G →* L) → G → L) _ _ _ := by
   -- Porting note: Some casts are required.
   letI := Classical.decEq (G →* L);

feat: short exact sequence of free modules (#6360)

We prove that if the left and right term in a short exact sequence of modules are free, then the middle term is free as well, and related results.

d3bfbe43

Diff

@@ -220,6 +220,38 @@ theorem LinearIndependent.map (hv : LinearIndependent R v) {f : M →ₗ[R] M'}
   exact fun _ => rfl
 #align linear_independent.map LinearIndependent.map
 
+/-- If `v` is an injective family of vectors such that `f ∘ v` is linearly independent, then `v`
+    spans a submodule disjoint from the kernel of `f` -/
+theorem Submodule.ker_range_disjoint {f : M →ₗ[R] M'} (hi : v.Injective)
+    (hv : LinearIndependent R (f ∘ v)) :
+    Disjoint (LinearMap.ker f) (Submodule.span R (Set.range v)) := by
+  rw [Submodule.disjoint_def]
+  intro m hm hmr
+  simp only [LinearMap.mem_ker] at hm
+  rw [mem_span_set] at hmr
+  obtain ⟨c, ⟨hc, hsum⟩⟩ := hmr
+  rw [← hsum, map_finsupp_sum] at hm
+  simp_rw [f.map_smul] at hm
+  dsimp [Finsupp.sum] at hm
+  rw [linearIndependent_iff'] at hv
+  specialize hv (Finset.preimage c.support v (Set.injOn_of_injective hi _))
+  rw [← Finset.sum_preimage v c.support (Set.injOn_of_injective hi _) _ _] at hm
+  · rw [← hsum]
+    apply Finset.sum_eq_zero
+    intro x hx
+    obtain ⟨y, hy⟩ := hc hx
+    rw [← hy]
+    have : c (v y) = 0
+    · apply hv (c ∘ v) hm y
+      simp only [Finset.mem_preimage, Function.comp_apply]
+      dsimp at hy
+      rwa [hy]
+    rw [this]
+    simp only [zero_smul]
+  · intro x hx hnx
+    exfalso
+    exact hnx (hc hx)
+
 /-- An injective linear map sends linearly independent families of vectors to linearly independent
 families of vectors. See also `LinearIndependent.map` for a more general statement. -/
 theorem LinearIndependent.map' (hv : LinearIndependent R v) (f : M →ₗ[R] M')

chore(LinearAlgebra): remove open Classical (#6320)

This uncovers a few situations where a lemma was stated with the wrong decidability assumption. The corrected lemmas are strictly more syntactically-general.

This is exhaustive in the LinearAlgebra folder.

Where removal is impractical, this switches to open Classical in to make the intent clear.

73993336

Diff

@@ -77,7 +77,7 @@ noncomputable section
 
 open Function Set Submodule
 
-open Classical BigOperators Cardinal
+open BigOperators Cardinal
 
 universe u' u
 
@@ -132,8 +132,9 @@ theorem linearIndependent_iff' :
 theorem linearIndependent_iff'' :
     LinearIndependent R v ↔
       ∀ (s : Finset ι) (g : ι → R) (_hg : ∀ (i) (_ : i ∉ s), g i = 0),
-        ∑ i in s, g i • v i = 0 → ∀ i, g i = 0 :=
-  linearIndependent_iff'.trans
+        ∑ i in s, g i • v i = 0 → ∀ i, g i = 0 := by
+  classical
+  exact linearIndependent_iff'.trans
     ⟨fun H s g hg hv i => if his : i ∈ s then H s g hv i his else hg i his, fun H s g hg i hi => by
       convert
         H s (fun j => if j ∈ s then g j else 0) (fun j hj => if_neg hj)
@@ -160,7 +161,7 @@ theorem Fintype.linearIndependent_iff [Fintype ι] :
 
 /-- A finite family of vectors `v i` is linear independent iff the linear map that sends
 `c : ι → R` to `∑ i, c i • v i` has the trivial kernel. -/
-theorem Fintype.linearIndependent_iff' [Fintype ι] :
+theorem Fintype.linearIndependent_iff' [Fintype ι] [DecidableEq ι] :
     LinearIndependent R v ↔
       LinearMap.ker (LinearMap.lsum R (fun _ ↦ R) ℕ fun i ↦ LinearMap.id.smulRight (v i)) = ⊥ :=
   by simp [Fintype.linearIndependent_iff, LinearMap.ker_eq_bot', funext_iff]
@@ -642,6 +643,7 @@ theorem linearIndependent_sum {v : Sum ι ι' → M} :
         LinearIndependent R (v ∘ Sum.inr) ∧
           Disjoint (Submodule.span R (range (v ∘ Sum.inl)))
             (Submodule.span R (range (v ∘ Sum.inr))) := by
+  classical
   rw [range_comp v, range_comp v]
   refine' ⟨_, _⟩
   · intro h
@@ -693,6 +695,7 @@ theorem linearIndependent_iUnion_finite_subtype {ι : Type _} {f : ι → Set M}
     (hl : ∀ i, LinearIndependent R (fun x => x : f i → M))
     (hd : ∀ i, ∀ t : Set ι, t.Finite → i ∉ t → Disjoint (span R (f i)) (⨆ i ∈ t, span R (f i))) :
     LinearIndependent R (fun x => x : (⋃ i, f i) → M) := by
+  classical
   rw [iUnion_eq_iUnion_finset f]
   apply linearIndependent_iUnion_of_directed
   · apply directed_of_sup
@@ -1204,6 +1207,7 @@ theorem linearIndependent_option {v : Option ι → V} :
 theorem linearIndependent_insert' {ι} {s : Set ι} {a : ι} {f : ι → V} (has : a ∉ s) :
     (LinearIndependent K fun x : ↥(insert a s) => f x) ↔
       (LinearIndependent K fun x : s => f x) ∧ f a ∉ Submodule.span K (f '' s) := by
+  classical
   rw [← linearIndependent_equiv ((Equiv.optionEquivSumPUnit _).trans (Equiv.Set.insert has).symm),
     linearIndependent_option]
   -- Porting note: `simp [(· ∘ ·), range_comp f]` → `simp [(· ∘ ·)]; erw [range_comp f ..]; simp`
@@ -1334,6 +1338,7 @@ theorem LinearIndependent.linearIndependent_extend (hs : LinearIndependent K (fu
 theorem exists_of_linearIndependent_of_finite_span {t : Finset V}
     (hs : LinearIndependent K (fun x => x : s → V)) (hst : s ⊆ (span K ↑t : Submodule K V)) :
     ∃ t' : Finset V, ↑t' ⊆ s ∪ ↑t ∧ s ⊆ ↑t' ∧ t'.card = t.card := by
+  classical
   have :
     ∀ t : Finset V,
       ∀ s' : Finset V,

chore(*): add protected to *.insert theorems (#6142)

Otherwise code like

theorem ContMDiffWithinAt.mythm (h : x ∈ insert y s) : _ = _

interprets insert as ContMDiffWithinAt.insert, not Insert.insert.

9f14c412

Diff

@@ -1169,7 +1169,7 @@ theorem linearIndependent_iff_not_mem_span :
     exact False.elim (h _ ((smul_mem_iff _ ha').1 ha))
 #align linear_independent_iff_not_mem_span linearIndependent_iff_not_mem_span
 
-theorem LinearIndependent.insert (hs : LinearIndependent K (fun b => b : s → V))
+protected theorem LinearIndependent.insert (hs : LinearIndependent K (fun b => b : s → V))
     (hx : x ∉ span K s) : LinearIndependent K (fun b => b : ↥(insert x s) → V) := by
   rw [← union_singleton]
   have x0 : x ≠ 0 := mt (by rintro rfl; apply zero_mem (span K s)) hx

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp, Anne Baanen
-
-! This file was ported from Lean 3 source module linear_algebra.linear_independent
-! leanprover-community/mathlib commit 9d684a893c52e1d6692a504a118bfccbae04feeb
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.BigOperators.Fin
 import Mathlib.LinearAlgebra.Finsupp
 import Mathlib.LinearAlgebra.Prod
 import Mathlib.SetTheory.Cardinal.Basic
 
+#align_import linear_algebra.linear_independent from "leanprover-community/mathlib"@"9d684a893c52e1d6692a504a118bfccbae04feeb"
+
 /-!
 
 # Linear independence

fix: precedence of # (#5623)

d450fcd7

Diff

@@ -333,7 +333,7 @@ then the same is true for arbitrary sets of linearly independent vectors.
 -/
 theorem linearIndependent_bounded_of_finset_linearIndependent_bounded {n : ℕ}
     (H : ∀ s : Finset M, (LinearIndependent R fun i : s => (i : M)) → s.card ≤ n) :
-    ∀ s : Set M, LinearIndependent R ((↑) : s → M) → (#s) ≤ n := by
+    ∀ s : Set M, LinearIndependent R ((↑) : s → M) → #s ≤ n := by
   intro s li
   apply Cardinal.card_le_of
   intro t

fix: ∑' precedence (#5615)

Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) $([∑∏][^()∑∏]*,[^()∑∏:]*)$ ([⊂⊆=<≤]) replaced by $1 $2 $3

03fc68aa

Diff

@@ -109,7 +109,7 @@ theorem linearIndependent_iff : LinearIndependent R v ↔ ∀ l, Finsupp.total 
 
 theorem linearIndependent_iff' :
     LinearIndependent R v ↔
-      ∀ s : Finset ι, ∀ g : ι → R, (∑ i in s, g i • v i) = 0 → ∀ i ∈ s, g i = 0 :=
+      ∀ s : Finset ι, ∀ g : ι → R, ∑ i in s, g i • v i = 0 → ∀ i ∈ s, g i = 0 :=
   linearIndependent_iff.trans
     ⟨fun hf s g hg i his =>
       have h :=
@@ -135,7 +135,7 @@ theorem linearIndependent_iff' :
 theorem linearIndependent_iff'' :
     LinearIndependent R v ↔
       ∀ (s : Finset ι) (g : ι → R) (_hg : ∀ (i) (_ : i ∉ s), g i = 0),
-        (∑ i in s, g i • v i) = 0 → ∀ i, g i = 0 :=
+        ∑ i in s, g i • v i = 0 → ∀ i, g i = 0 :=
   linearIndependent_iff'.trans
     ⟨fun H s g hg hv i => if his : i ∈ s then H s g hv i his else hg i his, fun H s g hg i hi => by
       convert
@@ -146,13 +146,13 @@ theorem linearIndependent_iff'' :
 
 theorem not_linearIndependent_iff :
     ¬LinearIndependent R v ↔
-      ∃ s : Finset ι, ∃ g : ι → R, (∑ i in s, g i • v i) = 0 ∧ ∃ i ∈ s, g i ≠ 0 := by
+      ∃ s : Finset ι, ∃ g : ι → R, ∑ i in s, g i • v i = 0 ∧ ∃ i ∈ s, g i ≠ 0 := by
   rw [linearIndependent_iff']
   simp only [exists_prop, not_forall]
 #align not_linear_independent_iff not_linearIndependent_iff
 
 theorem Fintype.linearIndependent_iff [Fintype ι] :
-    LinearIndependent R v ↔ ∀ g : ι → R, (∑ i, g i • v i) = 0 → ∀ i, g i = 0 := by
+    LinearIndependent R v ↔ ∀ g : ι → R, ∑ i, g i • v i = 0 → ∀ i, g i = 0 := by
   refine'
     ⟨fun H g => by simpa using linearIndependent_iff'.1 H Finset.univ g, fun H =>
       linearIndependent_iff''.2 fun s g hg hs i => H _ _ _⟩
@@ -170,7 +170,7 @@ theorem Fintype.linearIndependent_iff' [Fintype ι] :
 #align fintype.linear_independent_iff' Fintype.linearIndependent_iff'
 
 theorem Fintype.not_linearIndependent_iff [Fintype ι] :
-    ¬LinearIndependent R v ↔ ∃ g : ι → R, (∑ i, g i • v i) = 0 ∧ ∃ i, g i ≠ 0 := by
+    ¬LinearIndependent R v ↔ ∃ g : ι → R, ∑ i, g i • v i = 0 ∧ ∃ i, g i ≠ 0 := by
   simpa using not_iff_not.2 Fintype.linearIndependent_iff
 #align fintype.not_linear_independent_iff Fintype.not_linearIndependent_iff
 
@@ -374,7 +374,7 @@ theorem linearDependent_comp_subtype' {s : Set ι} :
 /-- A version of `linearDependent_comp_subtype'` with `Finsupp.total` unfolded. -/
 theorem linearDependent_comp_subtype {s : Set ι} :
     ¬LinearIndependent R (v ∘ (↑) : s → M) ↔
-      ∃ f : ι →₀ R, f ∈ Finsupp.supported R R s ∧ (∑ i in f.support, f i • v i) = 0 ∧ f ≠ 0 :=
+      ∃ f : ι →₀ R, f ∈ Finsupp.supported R R s ∧ ∑ i in f.support, f i • v i = 0 ∧ f ≠ 0 :=
   linearDependent_comp_subtype'
 #align linear_dependent_comp_subtype linearDependent_comp_subtype

feat(Data.Set.Basic/Data.Finset.Basic): rename insert_subset (#5450)

Currently, (for both Set and Finset) insert_subset is an iff lemma stating that insert a s ⊆ t if and only if a ∈ t and s ⊆ t. For both types, this PR renames this lemma to insert_subset_iff, and adds an insert_subset lemma that gives the implication just in the reverse direction : namely theorem insert_subset (ha : a ∈ t) (hs : s ⊆ t) : insert a s ⊆ t .

This both aligns the naming with union_subset and union_subset_iff, and removes the need for the awkward insert_subset.mpr ⟨_,_⟩ idiom. It touches a lot of files (too many to list), but in a trivial way.

d8b62864

Diff

@@ -1285,7 +1285,7 @@ theorem exists_linearIndependent_extension (hs : LinearIndependent K ((↑) : s
   · refine' ⟨b, bt, sb, fun x xt => _, bi⟩
     by_contra hn
     apply hn
-    rw [← h _ ⟨insert_subset.2 ⟨xt, bt⟩, bi.insert hn⟩ (subset_insert _ _)]
+    rw [← h _ ⟨insert_subset_iff.2 ⟨xt, bt⟩, bi.insert hn⟩ (subset_insert _ _)]
     exact subset_span (mem_insert _ _)
 #align exists_linear_independent_extension exists_linearIndependent_extension
 
@@ -1383,7 +1383,7 @@ theorem exists_of_linearIndependent_of_finite_span {t : Finset V}
           have hb₁ : b₁ ∈ span K (insert b₂ ↑(s' ∪ t)) := by
             exact mem_span_insert_exchange (this hb₂s) hb₂t
           rw [span_insert_eq_span hb₁] at hb₃; simpa using hb₃
-        let ⟨u, hust, hsu, eq⟩ := ih _ (by simp [insert_subset, hb₂s, hs']) hst this
+        let ⟨u, hust, hsu, eq⟩ := ih _ (by simp [insert_subset_iff, hb₂s, hs']) hst this
         -- Porting note: `hb₂t'` → `Finset.card_insert_of_not_mem hb₂t'`
         ⟨u, Subset.trans hust <| union_subset_union (Subset.refl _) (by simp [subset_insert]), hsu,
           by simp [eq, Finset.card_insert_of_not_mem hb₂t', hb₁t, hb₁s']⟩

chore: clean up spacing around at and goals (#5387)

Changes are of the form

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

2a870323

Diff

@@ -214,7 +214,7 @@ theorem LinearIndependent.map (hv : LinearIndependent R v) {f : M →ₗ[R] M'}
   rw [disjoint_iff_inf_le, ← Set.image_univ, Finsupp.span_image_eq_map_total,
     map_inf_eq_map_inf_comap, map_le_iff_le_comap, comap_bot, Finsupp.supported_univ, top_inf_eq]
       at hf_inj
-  unfold LinearIndependent at hv⊢
+  unfold LinearIndependent at hv ⊢
   rw [hv, le_bot_iff] at hf_inj
   haveI : Inhabited M := ⟨0⟩
   rw [Finsupp.total_comp, @Finsupp.lmapDomain_total _ _ R _ _ _ _ _ _ _ _ _ _ f, LinearMap.ker_comp,
@@ -285,7 +285,7 @@ theorem linearIndependent_span (hs : LinearIndependent R v) :
 theorem LinearIndependent.fin_cons' {m : ℕ} (x : M) (v : Fin m → M) (hli : LinearIndependent R v)
     (x_ortho : ∀ (c : R) (y : Submodule.span R (Set.range v)), c • x + y = (0 : M) → c = 0) :
     LinearIndependent R (Fin.cons x v : Fin m.succ → M) := by
-  rw [Fintype.linearIndependent_iff] at hli⊢
+  rw [Fintype.linearIndependent_iff] at hli ⊢
   rintro g total_eq j
   simp_rw [Fin.sum_univ_succ, Fin.cons_zero, Fin.cons_succ] at total_eq
   have : g 0 = 0 := by
@@ -521,7 +521,7 @@ theorem LinearIndependent.image {ι} {s : Set ι} {f : ι → M}
 theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulAction G R]
     [DistribMulAction G M] [IsScalarTower G R M] [SMulCommClass G R M] {v : ι → M}
     (hv : LinearIndependent R v) (w : ι → G) : LinearIndependent R (w • v) := by
-  rw [linearIndependent_iff''] at hv⊢
+  rw [linearIndependent_iff''] at hv ⊢
   intro s g hgs hsum i
   refine' (smul_eq_zero_iff_eq (w i)).1 _
   refine' hv s (fun i => w i • g i) (fun i hi => _) _ i
@@ -536,7 +536,7 @@ theorem LinearIndependent.group_smul {G : Type _} [hG : Group G] [DistribMulActi
 -- `Rˣ` on `R` is not commutative.
 theorem LinearIndependent.units_smul {v : ι → M} (hv : LinearIndependent R v) (w : ι → Rˣ) :
     LinearIndependent R (w • v) := by
-  rw [linearIndependent_iff''] at hv⊢
+  rw [linearIndependent_iff''] at hv ⊢
   intro s g hgs hsum i
   rw [← (w i).mul_left_eq_zero]
   refine' hv s (fun i => g i • (w i : R)) (fun i hi => _) _ i
@@ -915,7 +915,7 @@ theorem exists_maximal_independent (s : ι → M) :
     have hfi : f i ≠ 0 := by
       contrapose hIlinind
       refine' linearDependent_comp_subtype.mpr ⟨f, _, sum_f, f_ne⟩
-      simp only [Finsupp.mem_supported, hJ] at supp_f⊢
+      simp only [Finsupp.mem_supported, hJ] at supp_f ⊢
       rintro x hx
       refine' (memJ.mp (supp_f hx)).resolve_left _
       rintro rfl

chore: reviewing porting notes about rw/simp/simp_rw (#5244)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

2145fc43

Diff

@@ -1241,6 +1241,8 @@ theorem linearIndependent_fin_snoc {n} {v : Fin n → V} :
       LinearIndependent K v ∧ x ∉ Submodule.span K (range v) := by
   -- Porting note: `rw` → `erw`
   -- https://github.com/leanprover-community/mathlib4/issues/5164
+  -- Here Lean can not see that `fun i ↦ Fin.cons x v (↑(finRotate (n + 1)) i)`
+  -- matches with `?f ∘ ↑(finRotate (n + 1))`.
   erw [Fin.snoc_eq_cons_rotate, linearIndependent_equiv, linearIndependent_fin_cons]
 #align linear_independent_fin_snoc linearIndependent_fin_snoc

chore: add links to issue for rw regressions (#5167)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

5307644a

Diff

@@ -1210,7 +1210,8 @@ theorem linearIndependent_insert' {ι} {s : Set ι} {a : ι} {f : ι → V} (has
   rw [← linearIndependent_equiv ((Equiv.optionEquivSumPUnit _).trans (Equiv.Set.insert has).symm),
     linearIndependent_option]
   -- Porting note: `simp [(· ∘ ·), range_comp f]` → `simp [(· ∘ ·)]; erw [range_comp f ..]; simp`
-  simp [(· ∘ ·)]
+  -- https://github.com/leanprover-community/mathlib4/issues/5164
+  simp only [(· ∘ ·)]
   erw [range_comp f ((↑) : s → ι)]
   simp
 #align linear_independent_insert' linearIndependent_insert'
@@ -1239,6 +1240,7 @@ theorem linearIndependent_fin_snoc {n} {v : Fin n → V} :
     LinearIndependent K (Fin.snoc v x : Fin (n + 1) → V) ↔
       LinearIndependent K v ∧ x ∉ Submodule.span K (range v) := by
   -- Porting note: `rw` → `erw`
+  -- https://github.com/leanprover-community/mathlib4/issues/5164
   erw [Fin.snoc_eq_cons_rotate, linearIndependent_equiv, linearIndependent_fin_cons]
 #align linear_independent_fin_snoc linearIndependent_fin_snoc

chore: fix backtick in docs (#5077)

I wrote a script to find lines that contain an odd number of backticks

878d95c4

Diff

@@ -48,7 +48,7 @@ vectors.
 * `linearIndependent_empty_type`: a family indexed by an empty type is linearly independent;
 * `linearIndependent_unique_iff`: if `ι` is a singleton, then `LinearIndependent K v` is
   equivalent to `v default ≠ 0`;
-* linearIndependent_option`, `linearIndependent_sum`, `linearIndependent_fin_cons`,
+* `linearIndependent_option`, `linearIndependent_sum`, `linearIndependent_fin_cons`,
   `linearIndependent_fin_succ`: type-specific tests for linear independence of families of vector
   fields;
 * `linearIndependent_insert`, `linearIndependent_union`, `linearIndependent_pair`,

chore: formatting issues (#4947)

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

5068808d

Diff

@@ -1268,7 +1268,7 @@ theorem linearIndependent_fin2 {f : Fin 2 → V} :
 #align linear_independent_fin2 linearIndependent_fin2
 
 theorem exists_linearIndependent_extension (hs : LinearIndependent K ((↑) : s → V)) (hst : s ⊆ t) :
-    ∃ (b : _)(_ : b ⊆ t), s ⊆ b ∧ t ⊆ span K b ∧ LinearIndependent K ((↑) : b → V) := by
+    ∃ (b : _) (_ : b ⊆ t), s ⊆ b ∧ t ⊆ span K b ∧ LinearIndependent K ((↑) : b → V) := by
   -- Porting note: The placeholder should be solved before `rcases`.
   have := by
     refine zorn_subset_nonempty { b | b ⊆ t ∧ LinearIndependent K ((↑) : b → V) } ?_ _ ⟨hst, hs⟩
@@ -1288,7 +1288,7 @@ theorem exists_linearIndependent_extension (hs : LinearIndependent K ((↑) : s
 variable (K t)
 
 theorem exists_linearIndependent :
-    ∃ (b : _)(_ : b ⊆ t), span K b = span K t ∧ LinearIndependent K ((↑) : b → V) := by
+    ∃ (b : _) (_ : b ⊆ t), span K b = span K t ∧ LinearIndependent K ((↑) : b → V) := by
   obtain ⟨b, hb₁, -, hb₂, hb₃⟩ :=
     exists_linearIndependent_extension (linearIndependent_empty K V) (Set.empty_subset t)
   exact ⟨b, hb₁, (span_eq_of_le _ hb₂ (Submodule.span_mono hb₁)).symm, hb₃⟩

chore: add space after exacts (#4945)

Too often tempted to change these during other PRs, so doing a mass edit here.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

bf799bb9

Diff

@@ -362,7 +362,7 @@ theorem linearIndependent_comp_subtype {s : Set ι} :
       intros
       assumption
     · rwa [Finsupp.embDomain_eq_mapDomain, Finsupp.sum_mapDomain_index]
-      exacts[fun _ => zero_smul _ _, fun _ _ _ => add_smul _ _ _]
+      exacts [fun _ => zero_smul _ _, fun _ _ _ => add_smul _ _ _]
 #align linear_independent_comp_subtype linearIndependent_comp_subtype
 
 theorem linearDependent_comp_subtype' {s : Set ι} :

style: allow _ for an argument in notation3 & replace _foo with _ in notation3 (#4652)

e2b5ca37

Diff

@@ -876,7 +876,7 @@ theorem exists_maximal_independent' (s : ι → M) :
   let indep : Set ι → Prop := fun I => LinearIndependent R (s ∘ (↑) : I → M)
   let X := { I : Set ι // indep I }
   let r : X → X → Prop := fun I J => I.1 ⊆ J.1
-  have key : ∀ c : Set X, IsChain r c → indep (⋃ (I : X) (_H : I ∈ c), I) := by
+  have key : ∀ c : Set X, IsChain r c → indep (⋃ (I : X) (_ : I ∈ c), I) := by
     intro c hc
     dsimp
     rw [linearIndependent_comp_subtype]

chore: fix upper/lowercase in comments (#4360)

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

27d257fc

Diff

@@ -44,7 +44,7 @@ vectors.
 
 * `Fintype.linearIndependent_iff`: if `ι` is a finite type, then any function `f : ι → R` has
   finite support, so we can reformulate the statement using `∑ i : ι, f i • v i` instead of a sum
-  over an auxiliary `s : finset ι`;
+  over an auxiliary `s : Finset ι`;
 * `linearIndependent_empty_type`: a family indexed by an empty type is linearly independent;
 * `linearIndependent_unique_iff`: if `ι` is a singleton, then `LinearIndependent K v` is
   equivalent to `v default ≠ 0`;

chore: update std 05-22 (#4248)

The main breaking change is that tac <;> [t1, t2] is now written tac <;> [t1; t2], to avoid clashing with tactics like cases and use that take comma-separated lists.

ac36b28e

Diff

@@ -982,7 +982,7 @@ theorem LinearIndependent.inl_union_inr {s : Set M} {t : Set M'}
     (hs : LinearIndependent R (fun x => x : s → M))
     (ht : LinearIndependent R (fun x => x : t → M')) :
     LinearIndependent R (fun x => x : ↥(inl R M M' '' s ∪ inr R M M' '' t) → M × M') := by
-  refine' (hs.image_subtype _).union (ht.image_subtype _) _ <;> [simp, simp, skip]
+  refine' (hs.image_subtype _).union (ht.image_subtype _) _ <;> [simp; simp; skip]
   simp only [span_image]
   simp [disjoint_iff, prod_inf_prod]
 #align linear_independent.inl_union_inr LinearIndependent.inl_union_inr

chore: reenable eta, bump to nightly 2023-05-16 (#3414)

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

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

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

a6e1045f

Diff

@@ -473,7 +473,6 @@ variable [Ring R] [AddCommGroup M] [AddCommGroup M'] [AddCommGroup M'']
 variable [Module R M] [Module R M'] [Module R M'']
 variable {a b : R} {x y : M}
 
-set_option synthInstance.etaExperiment true in
 theorem linearIndependent_iff_injective_total :
     LinearIndependent R v ↔ Function.Injective (Finsupp.total ι M R v) :=
   linearIndependent_iff.trans
@@ -609,7 +608,6 @@ section Subtype
 
 /-! The following lemmas use the subtype defined by a set in `M` as the index set `ι`. -/
 
-set_option synthInstance.etaExperiment true in
 theorem LinearIndependent.disjoint_span_image (hv : LinearIndependent R v) {s t : Set ι}
     (hs : Disjoint s t) : Disjoint (Submodule.span R <| v '' s) (Submodule.span R <| v '' t) := by
   simp only [disjoint_def, Finsupp.mem_span_image_iff_total]
@@ -630,7 +628,6 @@ theorem LinearIndependent.not_mem_span_image [Nontrivial R] (hv : LinearIndepend
   simpa using h
 #align linear_independent.not_mem_span_image LinearIndependent.not_mem_span_image
 
-set_option synthInstance.etaExperiment true in
 theorem LinearIndependent.total_ne_of_not_mem_support [Nontrivial R] (hv : LinearIndependent R v)
     {x : ι} (f : ι →₀ R) (h : x ∉ f.support) : Finsupp.total ι M R v f ≠ v x := by
   replace h : x ∉ (f.support : Set ι) := h
@@ -745,7 +742,6 @@ section repr
 
 variable (hv : LinearIndependent R v)
 
-set_option synthInstance.etaExperiment true in
 /-- Canonical isomorphism between linear combinations and the span of linearly independent vectors.
 -/
 @[simps (config := { rhsMd := default }) symm_apply]
@@ -765,7 +761,6 @@ def LinearIndependent.totalEquiv (hv : LinearIndependent R v) :
 #align linear_independent.total_equiv LinearIndependent.totalEquiv
 #align linear_independent.total_equiv_symm_apply LinearIndependent.totalEquiv_symm_apply
 
-set_option synthInstance.etaExperiment true in
 -- Porting note: The original theorem generated by `simps` was
 --               different from the theorem on Lean 3, and not simp-normal form.
 @[simp]
@@ -773,7 +768,6 @@ theorem LinearIndependent.totalEquiv_apply_coe (hv : LinearIndependent R v) (l :
     hv.totalEquiv l = Finsupp.total ι M R v l := rfl
 #align linear_independent.total_equiv_apply_coe LinearIndependent.totalEquiv_apply_coe
 
-set_option synthInstance.etaExperiment true in
 /-- Linear combination representing a vector in the span of linearly independent vectors.
 
 Given a family of linearly independent vectors, we can represent any vector in their span as
@@ -783,29 +777,24 @@ def LinearIndependent.repr (hv : LinearIndependent R v) : span R (range v) →
   hv.totalEquiv.symm
 #align linear_independent.repr LinearIndependent.repr
 
-set_option synthInstance.etaExperiment true in
 @[simp]
 theorem LinearIndependent.total_repr (x) : Finsupp.total ι M R v (hv.repr x) = x :=
   Subtype.ext_iff.1 (LinearEquiv.apply_symm_apply hv.totalEquiv x)
 #align linear_independent.total_repr LinearIndependent.total_repr
 
-set_option synthInstance.etaExperiment true in
 theorem LinearIndependent.total_comp_repr :
     (Finsupp.total ι M R v).comp hv.repr = Submodule.subtype _ :=
   LinearMap.ext <| hv.total_repr
 #align linear_independent.total_comp_repr LinearIndependent.total_comp_repr
 
-set_option synthInstance.etaExperiment true in
 theorem LinearIndependent.repr_ker : LinearMap.ker hv.repr = ⊥ := by
   rw [LinearIndependent.repr, LinearEquiv.ker]
 #align linear_independent.repr_ker LinearIndependent.repr_ker
 
-set_option synthInstance.etaExperiment true in
 theorem LinearIndependent.repr_range : LinearMap.range hv.repr = ⊤ := by
   rw [LinearIndependent.repr, LinearEquiv.range]
 #align linear_independent.repr_range LinearIndependent.repr_range
 
-set_option synthInstance.etaExperiment true in
 theorem LinearIndependent.repr_eq {l : ι →₀ R} {x : span R (range v)}
     (eq : Finsupp.total ι M R v l = ↑x) : hv.repr x = l := by
   have :
@@ -820,14 +809,12 @@ theorem LinearIndependent.repr_eq {l : ι →₀ R} {x : span R (range v)}
   rfl
 #align linear_independent.repr_eq LinearIndependent.repr_eq
 
-set_option synthInstance.etaExperiment true in
 theorem LinearIndependent.repr_eq_single (i) (x : span R (range v)) (hx : ↑x = v i) :
     hv.repr x = Finsupp.single i 1 := by
   apply hv.repr_eq
   simp [Finsupp.total_single, hx]
 #align linear_independent.repr_eq_single LinearIndependent.repr_eq_single
 
-set_option synthInstance.etaExperiment true in
 theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
     Span.repr R (Set.range v) x =
       (hv.repr x).equivMapDomain (Equiv.ofInjective _ hv.injective) := by
@@ -842,7 +829,6 @@ theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
   simp [← p]
 #align linear_independent.span_repr_eq LinearIndependent.span_repr_eq
 
-set_option synthInstance.etaExperiment true in
 theorem linearIndependent_iff_not_smul_mem_span :
     LinearIndependent R v ↔ ∀ (i : ι) (a : R), a • v i ∈ span R (v '' (univ \ {i})) → a = 0 :=
   ⟨fun hv i a ha => by
@@ -945,7 +931,6 @@ theorem exists_maximal_independent (s : ι → M) :
 
 end repr
 
-set_option synthInstance.etaExperiment true in
 theorem surjective_of_linearIndependent_of_span [Nontrivial R] (hv : LinearIndependent R v)
     (f : ι' ↪ ι) (hss : range v ⊆ span R (range (v ∘ f))) : Surjective f := by
   intro i
@@ -980,12 +965,10 @@ theorem eq_of_linearIndependent_of_span_subtype [Nontrivial R] {s t : Set M}
     rcases h_surj ⟨x, hx⟩ with ⟨y, hy⟩
     convert y.mem
     rw [← Subtype.mk.inj hy]
-    rfl
 #align eq_of_linear_independent_of_span_subtype eq_of_linearIndependent_of_span_subtype
 
 open LinearMap
 
-set_option synthInstance.etaExperiment true in
 theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
     (hs : LinearIndependent R (fun x => x : s → M))
     (hf_inj : Disjoint (span R s) (LinearMap.ker f)) :
@@ -1012,7 +995,6 @@ theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv :
       simp only [span_le, range_coe, range_comp_subset_range]
 #align linear_independent_inl_union_inr' linearIndependent_inl_union_inr'
 
-set_option synthInstance.etaExperiment true in
 -- See, for example, Keith Conrad's note
 --  <https://kconrad.math.uconn.edu/blurbs/galoistheory/linearchar.pdf>
 /-- Dedekind's linear independence of characters -/

chore: Rename to sSup/iSup (#3938)

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>

d1eb6264

Diff

@@ -430,34 +430,34 @@ theorem linearIndependent_of_finite (s : Set M)
     linearIndependent_subtype.1 (H _ hl (Finset.finite_toSet _)) l (Subset.refl _)
 #align linear_independent_of_finite linearIndependent_of_finite
 
-theorem linearIndependent_unionᵢ_of_directed {η : Type _} {s : η → Set M} (hs : Directed (· ⊆ ·) s)
+theorem linearIndependent_iUnion_of_directed {η : Type _} {s : η → Set M} (hs : Directed (· ⊆ ·) s)
     (h : ∀ i, LinearIndependent R (fun x => x : s i → M)) :
     LinearIndependent R (fun x => x : (⋃ i, s i) → M) := by
   by_cases hη : Nonempty η
   · skip
     refine' linearIndependent_of_finite (⋃ i, s i) fun t ht ft => _
-    rcases finite_subset_unionᵢ ft ht with ⟨I, fi, hI⟩
+    rcases finite_subset_iUnion ft ht with ⟨I, fi, hI⟩
     rcases hs.finset_le fi.toFinset with ⟨i, hi⟩
-    exact (h i).mono (Subset.trans hI <| unionᵢ₂_subset fun j hj => hi j (fi.mem_toFinset.2 hj))
-  · refine (linearIndependent_empty R M).mono (t := unionᵢ (s ·)) ?_
+    exact (h i).mono (Subset.trans hI <| iUnion₂_subset fun j hj => hi j (fi.mem_toFinset.2 hj))
+  · refine (linearIndependent_empty R M).mono (t := iUnion (s ·)) ?_
     rintro _ ⟨_, ⟨i, _⟩, _⟩
     exact hη ⟨i⟩
-#align linear_independent_Union_of_directed linearIndependent_unionᵢ_of_directed
+#align linear_independent_Union_of_directed linearIndependent_iUnion_of_directed
 
-theorem linearIndependent_unionₛ_of_directed {s : Set (Set M)} (hs : DirectedOn (· ⊆ ·) s)
+theorem linearIndependent_sUnion_of_directed {s : Set (Set M)} (hs : DirectedOn (· ⊆ ·) s)
     (h : ∀ a ∈ s, LinearIndependent R ((↑) : ((a : Set M) : Type _) → M)) :
     LinearIndependent R (fun x => x : ⋃₀ s → M) := by
-  rw [unionₛ_eq_unionᵢ];
-    exact linearIndependent_unionᵢ_of_directed hs.directed_val (by simpa using h)
-#align linear_independent_sUnion_of_directed linearIndependent_unionₛ_of_directed
+  rw [sUnion_eq_iUnion];
+    exact linearIndependent_iUnion_of_directed hs.directed_val (by simpa using h)
+#align linear_independent_sUnion_of_directed linearIndependent_sUnion_of_directed
 
-theorem linearIndependent_bunionᵢ_of_directed {η} {s : Set η} {t : η → Set M}
+theorem linearIndependent_biUnion_of_directed {η} {s : Set η} {t : η → Set M}
     (hs : DirectedOn (t ⁻¹'o (· ⊆ ·)) s) (h : ∀ a ∈ s, LinearIndependent R (fun x => x : t a → M)) :
     LinearIndependent R (fun x => x : (⋃ a ∈ s, t a) → M) := by
-  rw [bunionᵢ_eq_unionᵢ]
+  rw [biUnion_eq_iUnion]
   exact
-    linearIndependent_unionᵢ_of_directed (directed_comp.2 <| hs.directed_val) (by simpa using h)
-#align linear_independent_bUnion_of_directed linearIndependent_bunionᵢ_of_directed
+    linearIndependent_iUnion_of_directed (directed_comp.2 <| hs.directed_val) (by simpa using h)
+#align linear_independent_bUnion_of_directed linearIndependent_biUnion_of_directed
 
 end Subtype
 
@@ -695,25 +695,25 @@ theorem LinearIndependent.union {s t : Set M} (hs : LinearIndependent R (fun x =
   (hs.sum_type ht <| by simpa).to_subtype_range' <| by simp
 #align linear_independent.union LinearIndependent.union
 
-theorem linearIndependent_unionᵢ_finite_subtype {ι : Type _} {f : ι → Set M}
+theorem linearIndependent_iUnion_finite_subtype {ι : Type _} {f : ι → Set M}
     (hl : ∀ i, LinearIndependent R (fun x => x : f i → M))
     (hd : ∀ i, ∀ t : Set ι, t.Finite → i ∉ t → Disjoint (span R (f i)) (⨆ i ∈ t, span R (f i))) :
     LinearIndependent R (fun x => x : (⋃ i, f i) → M) := by
-  rw [unionᵢ_eq_unionᵢ_finset f]
-  apply linearIndependent_unionᵢ_of_directed
+  rw [iUnion_eq_iUnion_finset f]
+  apply linearIndependent_iUnion_of_directed
   · apply directed_of_sup
-    exact fun t₁ t₂ ht => unionᵢ_mono fun i => unionᵢ_subset_unionᵢ_const fun h => ht h
+    exact fun t₁ t₂ ht => iUnion_mono fun i => iUnion_subset_iUnion_const fun h => ht h
   intro t
   induction' t using Finset.induction_on with i s his ih
   · refine' (linearIndependent_empty R M).mono _
     simp
-  · rw [Finset.set_bunionᵢ_insert]
+  · rw [Finset.set_biUnion_insert]
     refine' (hl _).union ih _
-    rw [span_unionᵢ₂]
+    rw [span_iUnion₂]
     exact hd i s s.finite_toSet his
-#align linear_independent_Union_finite_subtype linearIndependent_unionᵢ_finite_subtype
+#align linear_independent_Union_finite_subtype linearIndependent_iUnion_finite_subtype
 
-theorem linearIndependent_unionᵢ_finite {η : Type _} {ιs : η → Type _} {f : ∀ j : η, ιs j → M}
+theorem linearIndependent_iUnion_finite {η : Type _} {ιs : η → Type _} {f : ∀ j : η, ιs j → M}
     (hindep : ∀ j, LinearIndependent R (f j))
     (hd : ∀ i, ∀ t : Set η,
       t.Finite → i ∉ t → Disjoint (span R (range (f i))) (⨆ i ∈ t, span R (range (f i)))) :
@@ -730,14 +730,14 @@ theorem linearIndependent_unionᵢ_finite {η : Type _} {ιs : η → Type _} {f
         apply
           disjoint_def.1 (hd x₁ {y₁} (finite_singleton y₁) fun h => h_cases (eq_of_mem_singleton h))
             (f x₁ x₂) (subset_span (mem_range_self _))
-        rw [supᵢ_singleton]
+        rw [iSup_singleton]
         simp only at hxy
         rw [hxy]
         exact subset_span (mem_range_self y₂)
       exact False.elim ((hindep x₁).ne_zero _ h0)
-  rw [range_sigma_eq_unionᵢ_range]
-  apply linearIndependent_unionᵢ_finite_subtype (fun j => (hindep j).to_subtype_range) hd
-#align linear_independent_Union_finite linearIndependent_unionᵢ_finite
+  rw [range_sigma_eq_iUnion_range]
+  apply linearIndependent_iUnion_finite_subtype (fun j => (hindep j).to_subtype_range) hd
+#align linear_independent_Union_finite linearIndependent_iUnion_finite
 
 end Subtype
 
@@ -871,7 +871,7 @@ theorem LinearIndependent.independent_span_singleton (hv : LinearIndependent R v
   refine' CompleteLattice.independent_def.mp fun i => _
   rw [disjoint_iff_inf_le]
   intro m hm
-  simp only [mem_inf, mem_span_singleton, supᵢ_subtype', ← span_range_eq_supᵢ] at hm
+  simp only [mem_inf, mem_span_singleton, iSup_subtype', ← span_range_eq_iSup] at hm
   obtain ⟨⟨r, rfl⟩, hm⟩ := hm
   suffices r = 0 by simp [this]
   apply linearIndependent_iff_not_smul_mem_span.mp hv i
@@ -899,12 +899,12 @@ theorem exists_maximal_independent' (s : ι → M) :
     · simpa using hsupport
     haveI : IsRefl X r := ⟨fun _ => Set.Subset.refl _⟩
     obtain ⟨I, _I_mem, hI⟩ : ∃ I ∈ c, (f.support : Set ι) ⊆ I :=
-      hc.directedOn.exists_mem_subset_of_finset_subset_bunionᵢ hn hsupport
+      hc.directedOn.exists_mem_subset_of_finset_subset_biUnion hn hsupport
     exact linearIndependent_comp_subtype.mp I.2 f hI hsum
   have trans : Transitive r := fun I J K => Set.Subset.trans
   obtain ⟨⟨I, hli : indep I⟩, hmax : ∀ a, r ⟨I, hli⟩ a → r a ⟨I, hli⟩⟩ :=
     @exists_maximal_of_chains_bounded _ r
-      (fun c hc => ⟨⟨⋃ I ∈ c, (I : Set ι), key c hc⟩, fun I => Set.subset_bunionᵢ_of_mem⟩) @trans
+      (fun c hc => ⟨⟨⋃ I ∈ c, (I : Set ι), key c hc⟩, fun I => Set.subset_biUnion_of_mem⟩) @trans
   exact ⟨I, hli, fun J hsub hli => Set.Subset.antisymm hsub (hmax ⟨J, hli⟩ hsub)⟩
 #align exists_maximal_independent' exists_maximal_independent'
 
@@ -1291,9 +1291,9 @@ theorem exists_linearIndependent_extension (hs : LinearIndependent K ((↑) : s
   have := by
     refine zorn_subset_nonempty { b | b ⊆ t ∧ LinearIndependent K ((↑) : b → V) } ?_ _ ⟨hst, hs⟩
     · refine' fun c hc cc _c0 => ⟨⋃₀ c, ⟨_, _⟩, fun x => _⟩
-      · exact unionₛ_subset fun x xc => (hc xc).1
-      · exact linearIndependent_unionₛ_of_directed cc.directedOn fun x xc => (hc xc).2
-      · exact subset_unionₛ_of_mem
+      · exact sUnion_subset fun x xc => (hc xc).1
+      · exact linearIndependent_sUnion_of_directed cc.directedOn fun x xc => (hc xc).2
+      · exact subset_sUnion_of_mem
   rcases this with
     ⟨b, ⟨bt, bi⟩, sb, h⟩
   · refine' ⟨b, bt, sb, fun x xt => _, bi⟩

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -137,8 +137,7 @@ theorem linearIndependent_iff'' :
       ∀ (s : Finset ι) (g : ι → R) (_hg : ∀ (i) (_ : i ∉ s), g i = 0),
         (∑ i in s, g i • v i) = 0 → ∀ i, g i = 0 :=
   linearIndependent_iff'.trans
-    ⟨fun H s g hg hv i => if his : i ∈ s then H s g hv i his else hg i his, fun H s g hg i hi =>
-      by
+    ⟨fun H s g hg hv i => if his : i ∈ s then H s g hv i his else hg i his, fun H s g hg i hi => by
       convert
         H s (fun j => if j ∈ s then g j else 0) (fun j hj => if_neg hj)
           (by simp_rw [ite_smul, zero_smul, Finset.sum_extend_by_zero, hg]) i
@@ -289,8 +288,7 @@ theorem LinearIndependent.fin_cons' {m : ℕ} (x : M) (v : Fin m → M) (hli : L
   rw [Fintype.linearIndependent_iff] at hli⊢
   rintro g total_eq j
   simp_rw [Fin.sum_univ_succ, Fin.cons_zero, Fin.cons_succ] at total_eq
-  have : g 0 = 0 :=
-    by
+  have : g 0 = 0 := by
     refine' x_ortho (g 0) ⟨∑ i : Fin m, g i.succ • v i, _⟩ total_eq
     exact sum_mem fun i _ => smul_mem _ _ (subset_span ⟨i, rfl⟩)
   rw [this, zero_smul, zero_add] at total_eq
@@ -488,12 +486,10 @@ alias linearIndependent_iff_injective_total ↔ LinearIndependent.injective_tota
 theorem LinearIndependent.injective [Nontrivial R] (hv : LinearIndependent R v) : Injective v := by
   intro i j hij
   let l : ι →₀ R := Finsupp.single i (1 : R) - Finsupp.single j 1
-  have h_total : Finsupp.total ι M R v l = 0 :=
-    by
+  have h_total : Finsupp.total ι M R v l = 0 := by
     simp_rw [LinearMap.map_sub, Finsupp.total_apply]
     simp [hij]
-  have h_single_eq : Finsupp.single i (1 : R) = Finsupp.single j 1 :=
-    by
+  have h_single_eq : Finsupp.single i (1 : R) = Finsupp.single j 1 := by
     rw [linearIndependent_iff] at hv
     simp [eq_add_of_sub_eq' (hv l h_total)]
   simpa [Finsupp.single_eq_single_iff] using h_single_eq
@@ -511,8 +507,8 @@ theorem LinearIndependent.to_subtype_range' {ι} {f : ι → M} (hf : LinearInde
 #align linear_independent.to_subtype_range' LinearIndependent.to_subtype_range'
 
 theorem LinearIndependent.image_of_comp {ι ι'} (s : Set ι) (f : ι → ι') (g : ι' → M)
-    (hs : LinearIndependent R fun x : s => g (f x)) : LinearIndependent R fun x : f '' s => g x :=
-  by
+    (hs : LinearIndependent R fun x : s => g (f x)) :
+    LinearIndependent R fun x : f '' s => g x := by
   nontriviality R
   have : InjOn f s := injOn_iff_injective.2 hs.injective.of_comp
   exact (linearIndependent_equiv' (Equiv.Set.imageOfInjOn f s this) rfl).1 hs
@@ -598,12 +594,10 @@ theorem LinearIndependent.eq_of_smul_apply_eq_smul_apply {M : Type _} [AddCommGr
     {v : ι → M} (li : LinearIndependent R v) (c d : R) (i j : ι) (hc : c ≠ 0)
     (h : c • v i = d • v j) : i = j := by
   let l : ι →₀ R := Finsupp.single i c - Finsupp.single j d
-  have h_total : Finsupp.total ι M R v l = 0 :=
-    by
+  have h_total : Finsupp.total ι M R v l = 0 := by
     simp_rw [LinearMap.map_sub, Finsupp.total_apply]
     simp [h]
-  have h_single_eq : Finsupp.single i c = Finsupp.single j d :=
-    by
+  have h_single_eq : Finsupp.single i c = Finsupp.single j d := by
     rw [linearIndependent_iff] at li
     simp [eq_add_of_sub_eq' (li l h_total)]
   rcases (Finsupp.single_eq_single_iff _ _ _ _).mp h_single_eq with (⟨H, _⟩ | ⟨hc, _⟩)
@@ -627,8 +621,7 @@ theorem LinearIndependent.disjoint_span_image (hv : LinearIndependent R v) {s t
 
 theorem LinearIndependent.not_mem_span_image [Nontrivial R] (hv : LinearIndependent R v) {s : Set ι}
     {x : ι} (h : x ∉ s) : v x ∉ Submodule.span R (v '' s) := by
-  have h' : v x ∈ Submodule.span R (v '' {x}) :=
-    by
+  have h' : v x ∈ Submodule.span R (v '' {x}) := by
     rw [Set.image_singleton]
     exact mem_span_singleton_self (v x)
   intro w
@@ -733,8 +726,7 @@ theorem linearIndependent_unionᵢ_finite {η : Type _} {ιs : η → Type _} {f
     · apply Sigma.eq
       rw [LinearIndependent.injective (hindep _) hxy]
       rfl
-    · have h0 : f x₁ x₂ = 0 :=
-        by
+    · have h0 : f x₁ x₂ = 0 := by
         apply
           disjoint_def.1 (hd x₁ {y₁} (finite_singleton y₁) fun h => h_cases (eq_of_mem_singleton h))
             (f x₁ x₂) (subset_span (mem_range_self _))
@@ -898,8 +890,7 @@ theorem exists_maximal_independent' (s : ι → M) :
   let indep : Set ι → Prop := fun I => LinearIndependent R (s ∘ (↑) : I → M)
   let X := { I : Set ι // indep I }
   let r : X → X → Prop := fun I J => I.1 ⊆ J.1
-  have key : ∀ c : Set X, IsChain r c → indep (⋃ (I : X) (_H : I ∈ c), I) :=
-    by
+  have key : ∀ c : Set X, IsChain r c → indep (⋃ (I : X) (_H : I ∈ c), I) := by
     intro c hc
     dsimp
     rw [linearIndependent_comp_subtype]
@@ -960,8 +951,7 @@ theorem surjective_of_linearIndependent_of_span [Nontrivial R] (hv : LinearIndep
   intro i
   let repr : (span R (range (v ∘ f)) : Type _) → ι' →₀ R := (hv.comp f f.injective).repr
   let l := (repr ⟨v i, hss (mem_range_self i)⟩).mapDomain f
-  have h_total_l : Finsupp.total ι M R v l = v i :=
-    by
+  have h_total_l : Finsupp.total ι M R v l = v i := by
     dsimp only []
     rw [Finsupp.total_mapDomain]
     rw [(hv.comp f f.injective).total_repr]
@@ -1103,16 +1093,15 @@ theorem linearIndependent_monoidHom (G : Type _) [Monoid G] (L : Type _) [CommRi
           calc
             g a = g a * 1 := (mul_one _).symm
             _ = (g a • (a : G → L)) 1 := by rw [← a.map_one]; rfl
-            _ = (∑ i in insert a s, (g i • (i : G → L))) 1 :=
-              by
-                rw [Finset.sum_eq_single a]
-                · intro i his hia
-                  rw [Finset.mem_insert] at his
-                  rw [h3 i (his.resolve_left hia), zero_smul]
-                · intro haas
-                  exfalso
-                  apply haas
-                  exact Finset.mem_insert_self a s
+            _ = (∑ i in insert a s, (g i • (i : G → L))) 1 := by
+              rw [Finset.sum_eq_single a]
+              · intro i his hia
+                rw [Finset.mem_insert] at his
+                rw [h3 i (his.resolve_left hia), zero_smul]
+              · intro haas
+                exfalso
+                apply haas
+                exact Finset.mem_insert_self a s
             _ = 0 := by rw [hg]; rfl
         -- Now we're done; the last two facts together imply that `g` vanishes on every element
         -- of `insert a s`.
@@ -1375,8 +1364,7 @@ theorem exists_of_linearIndependent_of_finite_span {t : Finset V}
         have : s = ↑s' := eq_of_linearIndependent_of_span_subtype hs hs' <| by simpa using hss'
         ⟨s', by simp [this]⟩)
       fun b₁ t hb₁t ih s' hs' hst hss' =>
-      have hb₁s : b₁ ∉ s := fun h =>
-        by
+      have hb₁s : b₁ ∉ s := fun h => by
         have : b₁ ∈ s ∩ ↑(insert b₁ t) := ⟨h, Finset.mem_insert_self _ _⟩
         rwa [hst] at this
       have hb₁s' : b₁ ∉ s' := fun h => hb₁s <| hs' h
@@ -1413,8 +1401,7 @@ theorem exists_of_linearIndependent_of_finite_span {t : Finset V}
         -- Porting note: `hb₂t'` → `Finset.card_insert_of_not_mem hb₂t'`
         ⟨u, Subset.trans hust <| union_subset_union (Subset.refl _) (by simp [subset_insert]), hsu,
           by simp [eq, Finset.card_insert_of_not_mem hb₂t', hb₁t, hb₁s']⟩
-  have eq : ((t.filter fun x => x ∈ s) ∪ t.filter fun x => x ∉ s) = t :=
-    by
+  have eq : ((t.filter fun x => x ∈ s) ∪ t.filter fun x => x ∉ s) = t := by
     ext1 x
     by_cases x ∈ s <;> simp [*]
   apply

Match https://github.com/leanprover-community/mathlib/pull/18900

chore: Move lattice finset lemmas around (#3748)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

8988b247

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp, Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.linear_independent
-! leanprover-community/mathlib commit 6d584f1709bedbed9175bd9350df46599bdd7213
+! leanprover-community/mathlib commit 9d684a893c52e1d6692a504a118bfccbae04feeb
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -401,7 +401,7 @@ theorem linearIndependent_subtype_disjoint {s : Set M} :
 theorem linearIndependent_iff_totalOn {s : Set M} :
     LinearIndependent R (fun x => x : s → M) ↔
     (LinearMap.ker $ Finsupp.totalOn M M R id s) = ⊥ := by
-  rw [Finsupp.totalOn, LinearMap.ker, LinearMap.comap_codRestrict, map_bot, comap_bot,
+  rw [Finsupp.totalOn, LinearMap.ker, LinearMap.comap_codRestrict, Submodule.map_bot, comap_bot,
     LinearMap.ker_comp, linearIndependent_subtype_disjoint, disjoint_iff_inf_le, ←
     map_comap_subtype, map_le_iff_le_comap, comap_bot, ker_subtype, le_bot_iff]
 #align linear_independent_iff_total_on linearIndependent_iff_totalOn
@@ -768,7 +768,7 @@ def LinearIndependent.totalEquiv (hv : LinearIndependent R v) :
       rw [LinearMap.mem_range]
       apply mem_range_self l
   · rw [← LinearMap.range_eq_top, LinearMap.range_eq_map, LinearMap.map_codRestrict, ←
-      LinearMap.range_le_iff_comap, range_subtype, map_top]
+      LinearMap.range_le_iff_comap, range_subtype, Submodule.map_top]
     rw [Finsupp.range_total]
 #align linear_independent.total_equiv LinearIndependent.totalEquiv
 #align linear_independent.total_equiv_symm_apply LinearIndependent.totalEquiv_symm_apply

chore: use etaExperiment rather than hacking with instances (#3668)

This is to fix timeouts in https://github.com/leanprover-community/mathlib4/pull/3552.

See discussion at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/!4.233552.20.28LinearAlgebra.2EMatrix.2EToLin.29.

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

0f225a7f

Diff

@@ -475,12 +475,7 @@ variable [Ring R] [AddCommGroup M] [AddCommGroup M'] [AddCommGroup M'']
 variable [Module R M] [Module R M'] [Module R M'']
 variable {a b : R} {x y : M}
 
--- Porting note: TODO Erase this line. Needed because we don't have η for classes. (lean4#2074)
-attribute [-instance] Ring.toNonAssocRing
-
--- Porting note: added the following line, fails to be inferred otherwise. Probably lean4#2074
-instance : Module R R := Semiring.toModule
-
+set_option synthInstance.etaExperiment true in
 theorem linearIndependent_iff_injective_total :
     LinearIndependent R v ↔ Function.Injective (Finsupp.total ι M R v) :=
   linearIndependent_iff.trans
@@ -620,7 +615,7 @@ section Subtype
 
 /-! The following lemmas use the subtype defined by a set in `M` as the index set `ι`. -/
 
-
+set_option synthInstance.etaExperiment true in
 theorem LinearIndependent.disjoint_span_image (hv : LinearIndependent R v) {s t : Set ι}
     (hs : Disjoint s t) : Disjoint (Submodule.span R <| v '' s) (Submodule.span R <| v '' t) := by
   simp only [disjoint_def, Finsupp.mem_span_image_iff_total]
@@ -642,6 +637,7 @@ theorem LinearIndependent.not_mem_span_image [Nontrivial R] (hv : LinearIndepend
   simpa using h
 #align linear_independent.not_mem_span_image LinearIndependent.not_mem_span_image
 
+set_option synthInstance.etaExperiment true in
 theorem LinearIndependent.total_ne_of_not_mem_support [Nontrivial R] (hv : LinearIndependent R v)
     {x : ι} (f : ι →₀ R) (h : x ∉ f.support) : Finsupp.total ι M R v f ≠ v x := by
   replace h : x ∉ (f.support : Set ι) := h
@@ -757,6 +753,7 @@ section repr
 
 variable (hv : LinearIndependent R v)
 
+set_option synthInstance.etaExperiment true in
 /-- Canonical isomorphism between linear combinations and the span of linearly independent vectors.
 -/
 @[simps (config := { rhsMd := default }) symm_apply]
@@ -776,6 +773,7 @@ def LinearIndependent.totalEquiv (hv : LinearIndependent R v) :
 #align linear_independent.total_equiv LinearIndependent.totalEquiv
 #align linear_independent.total_equiv_symm_apply LinearIndependent.totalEquiv_symm_apply
 
+set_option synthInstance.etaExperiment true in
 -- Porting note: The original theorem generated by `simps` was
 --               different from the theorem on Lean 3, and not simp-normal form.
 @[simp]
@@ -783,6 +781,7 @@ theorem LinearIndependent.totalEquiv_apply_coe (hv : LinearIndependent R v) (l :
     hv.totalEquiv l = Finsupp.total ι M R v l := rfl
 #align linear_independent.total_equiv_apply_coe LinearIndependent.totalEquiv_apply_coe
 
+set_option synthInstance.etaExperiment true in
 /-- Linear combination representing a vector in the span of linearly independent vectors.
 
 Given a family of linearly independent vectors, we can represent any vector in their span as
@@ -792,24 +791,29 @@ def LinearIndependent.repr (hv : LinearIndependent R v) : span R (range v) →
   hv.totalEquiv.symm
 #align linear_independent.repr LinearIndependent.repr
 
+set_option synthInstance.etaExperiment true in
 @[simp]
 theorem LinearIndependent.total_repr (x) : Finsupp.total ι M R v (hv.repr x) = x :=
   Subtype.ext_iff.1 (LinearEquiv.apply_symm_apply hv.totalEquiv x)
 #align linear_independent.total_repr LinearIndependent.total_repr
 
+set_option synthInstance.etaExperiment true in
 theorem LinearIndependent.total_comp_repr :
     (Finsupp.total ι M R v).comp hv.repr = Submodule.subtype _ :=
   LinearMap.ext <| hv.total_repr
 #align linear_independent.total_comp_repr LinearIndependent.total_comp_repr
 
+set_option synthInstance.etaExperiment true in
 theorem LinearIndependent.repr_ker : LinearMap.ker hv.repr = ⊥ := by
   rw [LinearIndependent.repr, LinearEquiv.ker]
 #align linear_independent.repr_ker LinearIndependent.repr_ker
 
+set_option synthInstance.etaExperiment true in
 theorem LinearIndependent.repr_range : LinearMap.range hv.repr = ⊤ := by
   rw [LinearIndependent.repr, LinearEquiv.range]
 #align linear_independent.repr_range LinearIndependent.repr_range
 
+set_option synthInstance.etaExperiment true in
 theorem LinearIndependent.repr_eq {l : ι →₀ R} {x : span R (range v)}
     (eq : Finsupp.total ι M R v l = ↑x) : hv.repr x = l := by
   have :
@@ -824,12 +828,14 @@ theorem LinearIndependent.repr_eq {l : ι →₀ R} {x : span R (range v)}
   rfl
 #align linear_independent.repr_eq LinearIndependent.repr_eq
 
+set_option synthInstance.etaExperiment true in
 theorem LinearIndependent.repr_eq_single (i) (x : span R (range v)) (hx : ↑x = v i) :
     hv.repr x = Finsupp.single i 1 := by
   apply hv.repr_eq
   simp [Finsupp.total_single, hx]
 #align linear_independent.repr_eq_single LinearIndependent.repr_eq_single
 
+set_option synthInstance.etaExperiment true in
 theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
     Span.repr R (Set.range v) x =
       (hv.repr x).equivMapDomain (Equiv.ofInjective _ hv.injective) := by
@@ -844,7 +850,7 @@ theorem LinearIndependent.span_repr_eq [Nontrivial R] (x) :
   simp [← p]
 #align linear_independent.span_repr_eq LinearIndependent.span_repr_eq
 
--- TODO: why is this so slow?
+set_option synthInstance.etaExperiment true in
 theorem linearIndependent_iff_not_smul_mem_span :
     LinearIndependent R v ↔ ∀ (i : ι) (a : R), a • v i ∈ span R (v '' (univ \ {i})) → a = 0 :=
   ⟨fun hv i a ha => by
@@ -948,6 +954,7 @@ theorem exists_maximal_independent (s : ι → M) :
 
 end repr
 
+set_option synthInstance.etaExperiment true in
 theorem surjective_of_linearIndependent_of_span [Nontrivial R] (hv : LinearIndependent R v)
     (f : ι' ↪ ι) (hss : range v ⊆ span R (range (v ∘ f))) : Surjective f := by
   intro i
@@ -988,6 +995,7 @@ theorem eq_of_linearIndependent_of_span_subtype [Nontrivial R] {s t : Set M}
 
 open LinearMap
 
+set_option synthInstance.etaExperiment true in
 theorem LinearIndependent.image_subtype {s : Set M} {f : M →ₗ[R] M'}
     (hs : LinearIndependent R (fun x => x : s → M))
     (hf_inj : Disjoint (span R s) (LinearMap.ker f)) :
@@ -1014,6 +1022,7 @@ theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv :
       simp only [span_le, range_coe, range_comp_subset_range]
 #align linear_independent_inl_union_inr' linearIndependent_inl_union_inr'
 
+set_option synthInstance.etaExperiment true in
 -- See, for example, Keith Conrad's note
 --  <https://kconrad.math.uconn.edu/blurbs/galoistheory/linearchar.pdf>
 /-- Dedekind's linear independence of characters -/

fix: correct field names in IsCompl (#3661)

These are proofs not propositions so should be lowerCamelCase.

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

d9d4ff5c

Diff

@@ -665,7 +665,7 @@ theorem linearIndependent_sum {v : Sum ι ι' → M} :
     refine' ⟨h.comp _ Sum.inl_injective, h.comp _ Sum.inr_injective, _⟩
     refine' h.disjoint_span_image _
     -- Porting note: `isCompl_range_inl_range_inr.1` timeouts.
-    exact IsCompl.Disjoint isCompl_range_inl_range_inr
+    exact IsCompl.disjoint isCompl_range_inl_range_inr
   rintro ⟨hl, hr, hlr⟩
   rw [linearIndependent_iff'] at *
   intro s g hg i hi
@@ -680,7 +680,7 @@ theorem linearIndependent_sum {v : Sum ι ι' → M} :
     · -- Porting note: Here was one `exact`, but timeouted.
       refine Finset.disjoint_filter.2 fun x _ hx =>
         disjoint_left.1 ?_ hx
-      exact IsCompl.Disjoint isCompl_range_inl_range_inr
+      exact IsCompl.disjoint isCompl_range_inl_range_inr
   · rw [← eq_neg_iff_add_eq_zero] at this
     rw [disjoint_def'] at hlr
     have A := by
@@ -1010,7 +1010,7 @@ theorem linearIndependent_inl_union_inr' {v : ι → M} {v' : ι' → M'} (hv :
     (hv' : LinearIndependent R v') :
     LinearIndependent R (Sum.elim (inl R M M' ∘ v) (inr R M M' ∘ v')) :=
   (hv.map' (inl R M M') ker_inl).sum_type (hv'.map' (inr R M M') ker_inr) <| by
-    refine' isCompl_range_inl_inr.Disjoint.mono _ _ <;>
+    refine' isCompl_range_inl_inr.disjoint.mono _ _ <;>
       simp only [span_le, range_coe, range_comp_subset_range]
 #align linear_independent_inl_union_inr' linearIndependent_inl_union_inr'

fix: replace symmApply by symm_apply (#2560)

9aade17b

Diff

@@ -759,7 +759,7 @@ variable (hv : LinearIndependent R v)
 
 /-- Canonical isomorphism between linear combinations and the span of linearly independent vectors.
 -/
-@[simps (config := { rhsMd := default }) symmApply]
+@[simps (config := { rhsMd := default }) symm_apply]
 def LinearIndependent.totalEquiv (hv : LinearIndependent R v) :
     (ι →₀ R) ≃ₗ[R] span R (range v) := by
   apply LinearEquiv.ofBijective (LinearMap.codRestrict (span R (range v)) (Finsupp.total ι M R v) _)
@@ -774,7 +774,7 @@ def LinearIndependent.totalEquiv (hv : LinearIndependent R v) :
       LinearMap.range_le_iff_comap, range_subtype, map_top]
     rw [Finsupp.range_total]
 #align linear_independent.total_equiv LinearIndependent.totalEquiv
-#align linear_independent.total_equiv_symm_apply LinearIndependent.totalEquiv_symmApply
+#align linear_independent.total_equiv_symm_apply LinearIndependent.totalEquiv_symm_apply
 
 -- Porting note: The original theorem generated by `simps` was
 --               different from the theorem on Lean 3, and not simp-normal form.